Chapter 7 Resource Masters - Commack Schools 7 Worksheets.pdf · connected.mcgraw-hill.com...
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Chapter 7 Resource Masters
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CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish.
MHID ISBNStudy Guide and Intervention Workbook 0-07-660292-3 978-0-07-660292-6Homework Practice Workbook 0-07-660291-5 978-0-07-660291-9
Spanish VersionHomework Practice Workbook 0-07-660294-X 978-0-07-660294-0
Answers For Workbooks The answers for Chapter 7 of these workbooks can be found in the back of this Chapter Resource Masters booklet.
ConnectED All of the materials found in this booklet are included for viewing, printing, and editing at connected.mcgraw-hill.com.
Spanish Assessment Masters (MHID: 0-07-660289-3, ISBN: 978-0-07-660289-6) These masters contain a Spanish version of Chapter 7 Test Form 2A and Form 2C.
Copyright © by The McGraw-Hill Companies, Inc.
All rights reserved. The contents, or parts thereof, may be reproduced in print form for non-profit educational use with Glencoe Algebra 1, provided such reproductions bear copyright notice, but may not be reproduced in any form for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning.
Send all inquiries to:McGraw-Hill Education8787 Orion PlaceColumbus, OH 43240
ISBN: 978-0-07-660281-0MHID: 0-07-660281-8
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1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11
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ContentsTeacher’s Guide to Using the Chapter 7
Resource Masters .........................................iv
Chapter Resources Chapter 7 Student-Built Glossary ...................... 1Chapter 7 Anticipation Guide (English) ............. 3Chapter 7 Anticipation Guide (Spanish) ............ 4
Lesson 7-1Multiplication Properties of ExponentsStudy Guide and Intervention ............................ 5Skills Practice .................................................... 7Practice ............................................................. 8Word Problem Practice ...................................... 9Enrichment ...................................................... 10
Lesson 7-2Division Properties of ExponentsStudy Guide and Intervention ...........................11Skills Practice .................................................. 13Practice ........................................................... 14Word Problem Practice .................................... 15Enrichment ...................................................... 16
Lesson 7-3Rational ExponentsStudy Guide and Intervention .......................... 17Skills Practice .................................................. 19Practice ........................................................... 20Word Problem Practice .................................... 21Enrichment ...................................................... 22
Lesson 7-4Scientifi c NotationStudy Guide and Intervention .......................... 23Skills Practice .................................................. 25Practice ........................................................... 26Word Problem Practice .................................... 27Enrichment ...................................................... 28
Lesson 7-5Exponential FunctionsStudy Guide and Intervention .......................... 29Skills Practice .................................................. 31Practice ........................................................... 32Word Problem Practice .................................... 33Enrichment ...................................................... 34
Lesson 7-6Growth and DecayStudy Guide and Intervention .......................... 35Skills Practice .................................................. 37Practice ........................................................... 38Word Problem Practice .................................... 39Enrichment ...................................................... 40Spreadsheet Activity ........................................ 41
Lesson 7-7Geometric Sequences as Exponential FunctionsStudy Guide and Intervention .......................... 42Skills Practice .................................................. 44Practice ........................................................... 45Word Problem Practice .................................... 46Enrichment ...................................................... 47
Lesson 7-8Recursive FormulasStudy Guide and Intervention .......................... 48Skills Practice .................................................. 50Practice ........................................................... 51Word Problem Practice .................................... 52Enrichment ...................................................... 53
AssessmentStudent Recording Sheet ............................... 55Rubric for Scoring Extended Response .......... 56Chapter 7 Quizzes 1 and 2 ............................. 57Chapter 7 Quizzes 3 and 4 ............................. 58Chapter 7 Mid-Chapter Test ............................ 59Chapter 7 Vocabulary Test ............................... 60Chapter 7 Test, Form 1 .................................... 61Chapter 7 Test, Form 2A ................................. 63Chapter 7 Test, Form 2B ................................. 65Chapter 7 Test, Form 2C ................................. 67Chapter 7 Test, Form 2D ................................. 69Chapter 7 Test, Form 3 .................................... 71Chapter 7 Extended Response Test ................ 73Standardized Test Practice ...............................74
Answers ........................................... A1–A36
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Teacher’s Guide to Using the Chapter 7 Resource Masters
Chapter ResourcesStudent-Built Glossary (pages 1–2) These masters are a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. Give this to students before beginning Lesson 7-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.
Anticipation Guide (pages 3–4) This master, presented in both English and Spanish, is a survey used before beginning the chapter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their perceptions have changed.
Lesson ResourcesStudy Guide and Intervention These masters provide vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteaching activity. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.
Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the lesson.
Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for second-day teaching of the lesson.
Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.
Enrichment These activities may extend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. They are written for use with all levels of students.
Graphing Calculator, TI-Nspire, or Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation.
The Chapter 7 Resource Masters includes the core materials needed for Chapter 7. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing, printing, and editing at connectED.mcgraw-hill.com.
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Assessment OptionsThe assessment masters in the Chapter 7 Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment.
Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter.
Extended Response Rubric This master provides information for teachers and students on how to assess performance on open-ended questions.
Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter.
Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 11 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.
Leveled Chapter Tests• Form 1 contains multiple-choice ques-
tions and is intended for use with below grade level students.
• Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Form 3 is a free-response test for use with above grade level students.
All of the above mentioned tests include a free-response Bonus question.
Extended-Response Test Performance assessment tasks are suitable for all stu-dents. Sample answers and a scoring rubric are included for evaluation.
Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided as reduced pages.
• Full-size answer keys are provided for the assessment masters.
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Chapter 7 1 Glencoe Algebra 1
7 Student-Built Glossary
This is an alphabetical list of the key vocabulary terms you will learn in Chapter 7. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary TermFound
on PageDefi nition/Description/Example
binomialby·NOH·mee·uhl
constant
common ratio
compound interest
cube root
exponential decay function
exponential equation
exponential function
exponential growth function
(continued on the next page)
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Chapter 7 2 Glencoe Algebra 1
Student-Built Glossary (continued)7
Vocabulary TermFound
on PageDefi nition/Description/Example
geometric sequence
monomial mah·NOH·mee·uhl
negative exponent
nth root
order of magnitude
rational exponent
recursive formula
scientific notation
zero exponent
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Chapter 7 3 Glencoe Algebra 1
Anticipation GuideExponents and Exponential Functions
Before you begin Chapter 7
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).
STEP 1A, D, or NS
StatementSTEP 2A or D
1. When multiplying two powers that have the same base, multiply the exponents.
2. ( k 3 ) 4 is equivalent to k 12 .
3. To divide two powers that have the same base, subtract the exponents.
4. ( 2 − 5 )
3 is the same as 2 −
5 3 .
5. A polynomial may contain one or more monomials.
6. The degree of the polynomial 3 x 2 y 3 - 5y 2 + 8 x 3 is 3 because the greatest exponent is 3.
7. A function containing powers is called an exponential function.
8. Receiving compound interest on a bank account is one example of exponential growth.
After you complete Chapter 7
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.
7
Step 1
Step 2
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PDF 2nd
Capítulo 7 4 Álgebra 1 de Glencoe
Ejercicios preparatoriosExponentes y Funciones Exponenciales
7
Antes de comenzar el Capítulo 7
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a)).
PASO 1A, D o NS
EnunciadoPASO 2A o D
1. Al multiplicar dos potencias con la misma base, multiplica los exponentes.
2. ( k 3 ) 4 es equivalente a k 12 .
3. Para dividir dos potencias que tienen la misma base, resta los exponentes.
4. ( 2 − 5 )
3 es lo mismo que 2 −
5 3 .
5. Un polinomio puede contener uno o más monomios.
6. El grado del polinomio 3x 2 y 3 - 5y 2 + 8x 3 es 3 porque el exponente más grande es 3.
7. Una función que contiene potencias se denomina función exponencial.
8. El recibir interés compuesto en una cuenta bancaria es un ejemplo de crecimiento exponencial.
Después de completar el Capítulo 7
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D.
Paso 1
Paso 2
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Chapter 7 5 Glencoe Algebra 1
Study Guide and InterventionMultiplication Properties of Exponents
Multiply Monomials A monomial is a number, a variable, or the product of a number and one or more variables with nonnegative integer exponents. An expression of the form xn is called a power and represents the product you obtain when x is used as a factor n times. To multiply two powers that have the same base, add the exponents.
Product of Powers For any number a and all integers m and n, am ․ an = am + n.
Simplify (3x6)(5x2).(3x6)(5x2) = (3)(5)(x6 ․ x2) Group the coefficients
and the variables
= (3 ․ 5)(x6 + 2) Product of Powers
= 15x8 Simplify.
The product is 15x8.
Simplify (-4a3b)(3a2b5).(-4a3b)(3a2b5) = (-4)(3)(a3 ․ a2)(b ․ b5)
= -12(a3 + 2)(b1 + 5) = -12a5b6
The product is -12a5b6.
ExercisesSimplify each expression.
1. y(y5) 2. n2 ․ n7 3. (-7x2)(x4)
4. x(x2)(x4) 5. m ․ m5 6. (-x3)(-x4)
7. (2a2)(8a) 8. (rn)(rn3)(n2) 9. (x2y)(4xy3)
10. 1 − 3 ( 2a 3 b)( 6b 3 ) 11. (-4x3)(-5x7) 12. (-3j2k4)(2jk6)
13. ( 5a 2 bc 3 ) ( 1 − 5 abc 4 ) 14. (-5xy)(4x2)(y4) 15. (10x3yz2)(-2xy5z)
7-1
Example 1 Example 2
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Chapter 7 6 Glencoe Algebra 1
Simplify Expressions An expression of the form (xm)n is called a power of a power and represents the product you obtain when xm is used as a factor n times. To find the power of a power, multiply exponents.
Power of a Power For any number a and any integers m and p, (am)p = amp.
Power of a Product For any numbers a and b and any integer m, (ab)m = ambm.
We can combine and use these properties to simplify expressions involving monomials.
Simplify (-2ab2)3(a2)4.
(-2ab2)3(a2)4 = (-2ab2)3(a8) Power of a Power
= (-2)3(a3)(b2)3(a8) Power of a Product
= (-2)3(a3)(a8)(b2)3 Group the coefficients and the variables
= (-2)3(a11)(b2)3 Product of Powers
= -8a11b6 Power of a Power
The product is -8a11b6.
ExercisesSimplify each expression.
1. (y5)2 2. (n7)4 3. (x2)5(x3)
4. -3(ab4)3 5. (-3ab4)3 6. (4x2b)3
7. (4a2)2(b3) 8. (4x)2(b3) 9. (x2y4)5
10. (2a3b2)(b3)2 11. (-4xy)3(-2x2)3 12. (-3j2k3)2(2j2k)3
13. (25 a 2 b) 3 ( 1 − 5 abf)
2 14. (2xy)2(-3x2)(4y4) 15. (2x3y2z2)3(x2z)4
16. (-2n6y5)(-6n3y2)(ny)3 17. (-3a3n4)(-3a3n)4 18. -3(2x)4(4x5y)2
Study Guide and Intervention (continued)
Multiplication Properties of Exponents
7-1
Example
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Chapter 7 7 Glencoe Algebra 1
Skills PracticeMultiplication Properties of Exponents
Determine whether each expression is a monomial. Write yes or no. Explain.
1. 11
2. a - b
3. p 2
− r 2
4. y
5. j3k
6. 2a + 3b
Simplify.
7. a2(a3)(a6) 8. x(x2)(x7)
9. (y2z)(yz2) 10. (ℓ2k2)(ℓ3k)
11. (a2b4)(a2b2) 12. (cd2)(c3d2)
13. (2x2)(3x5) 14. (5a7)(4a2)
15. (4xy3)(3x3y5) 16. (7a5b2)(a2b3)
17. (-5m3)(3m8) 18. (-2c4d)(-4cd)
19. (102)3 20. (p3)12
21. (-6p)2 22. (-3y)3
23. (3pr2)2 24. (2b3c4)2
GEOMETRY Express the area of each figure as a monomial.
25.
x2
x5
26.
cd
cd
27.
4p
9p3
7-1
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Chapter 7 8 Glencoe Algebra 1
PracticeMultiplication Properties of Exponents
Determine whether each expression is a monomial. Write yes or no. Explain your reasoning.
1. 21 a 2 − 7b
2. b 3 c 2 − 2
Simplify each expression.
3. (-5x2y)(3x4) 4. (2ab2f 2)(4a3b2f 2)
5. (3ad4)(-2a2) 6. (4g3h)(-2g5)
7. (-15x y 4 ) (- 1 − 3 x y 3 ) 8. (-xy)3(xz)
9. (-18 m 2 n) 2 (- 1 − 6 m n 2 ) 10. (0.2a2b3)2
11. ( 2 − 3 p)
2 12. ( 1 −
4 a d 3 )
2
13. (0.4k3)3 14. [(42)2]2
GEOMETRY Express the area of each figure as a monomial.
15.
6a2b4
3ab2
16. 5x3
17.
6ab3
4a2b
GEOMETRY Express the volume of each solid as a monomial.
18.
3h23h2
3h2
19.
m3nmn3
n 20.
7g2
3g
21. COUNTING A panel of four light switches can be set in 24 ways. A panel of five light switches can set in twice this many ways. In how many ways can five light switches be set?
22. HOBBIES Tawa wants to increase her rock collection by a power of three this year and then increase it again by a power of two next year. If she has 2 rocks now, how many rocks will she have after the second year?
7-1
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Chapter 7 9 Glencoe Algebra 1
1. GRAVITY An egg that has been falling for x seconds has dropped at an average speed of 16x feet per second. If the egg is dropped from the top of a building, its total distance traveled is the product of the average rate times the time. Write a simplified expression to show the distance the egg has traveled after x seconds.
2. CIVIL ENGINEERING A developer is planning a sidewalk for a new development. The sidewalk can be installed in rectangular sections that have a fixed width of 3 feet and a length that can vary. Assuming that each section is the same length, express the area of a 4-section sidewalk as a monomial.
x
3 ft
3. PROBABILITY If you flip a coin 3 times in a row, there are 23 outcomes that can occur.
Outcomes
HHH TTT
HTT THH
HTH TTH
HHT THT
If you then flip the coin two more times, there are 23 × 22 outcomes that can occur. How many outcomes can occur if you flip the coin as mentioned above four more times? Write your answer in the form 2x.
4. SPORTS The volume of a sphere is given by the formula V = 4−
3 π r 3 , where r is the
radius of the sphere. Find the volume of air in three different basketballs. Use π = 3.14. Round your answers to the nearest whole number.
Ball Radius (in.) Volume (in3)
Child’s 4
Women’s 4.5
Men’s 4.8
5. ELECTRICITY An electrician uses the formula W = I2R , where W is the power in watts, I is the current in amperes, and R is the resistance in ohms.
a. Find the power in a household circuit that has 20 amperes of current and 5 ohms of resistance.
b. If the current is reduced by one half, what happens to the power?
Word Problem PracticeMultiplication Properties of Exponents
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Chapter 7 10 Glencoe Algebra 1
Enrichment
An Wang An Wang (1920–1990) was an Asian-American who became one of the pioneers of the computer industry in the United States. He grew up in Shanghai, China, but came to the United States to further his studies in science. In 1948, he invented a magnetic pulse controlling device that vastly increased the storage capacity of computers. He later founded his own company, Wang Laboratories, and became a leader in the development of desktop calculators and word processing systems. In 1988, Wang was elected to the National Inventors Hall of Fame.
Digital computers store information as numbers. Because the electronic circuits of a computer can exist in only one of two states, open or closed, the numbers that are stored can consist of only two digits, 0 or 1. Numbers written using only these two digits are called binary numbers. To find the decimal value of a binary number, you use the digits to write a polynomial in 2. For instance, this is how to find the decimal value of the number 10011012. (The subscript 2 indicates that this is a binary number.)
10011012 = 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20
= 1 × 64 + 0 × 32 + 0 × 16 + 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1= 64 + 0 + 0 + 8 + 4 + 0 + 1= 77
Find the decimal value of each binary number.
1. 11112 2. 100002 3. 110000112 4. 101110012
Write each decimal number as a binary number.
5. 8 6. 11 7. 29 8. 117
9. The chart at the right shows a set of decimal code numbers that is used widely in storing letters of the alphabet in a computer’s memory. Find the code numbers for the letters of your name. Then write the code for your name using binary numbers.
7-1
The American Standard Guide for
Information Interchange (ASCII)
A 65 N 78 a 97 n 110
B 66 O 79 b 98 o 111
C 67 P 80 c 99 p 112
D 68 Q 81 d 100 q 113
E 69 R 82 e 101 r 114
F 70 S 83 f 102 s 115
G 71 T 84 g 103 t 116
H 72 U 85 h 104 u 117
I 73 V 86 i 105 v 118
J 74 W 87 j 106 w 119
K 75 X 88 k 107 x 120
L 76 Y 89 l 108 y 121
M 77 Z 90 m 109 z 122
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Chapter 7 11 Glencoe Algebra 1
Study Guide and InterventionDivision Properties of Exponents
Divide Monomials To divide two powers with the same base, subtract the exponents.
Quotient of Powers For all integers m and n and any nonzero number a, a m − a n
= a m - n .
Power of a Quotient For any integer m and any real numbers a and b, b ≠ 0, ( a −
b )
m = a m −
b m .
Simplify a 4 b 7 −
ab 2 . Assume
that no denominator equals zero.
a 4 b 7 − ab 2
= ( a 4 − a ) ( b 7 − b 2
) Group powers with the same base.
= (a4 - 1)(b7 - 2) Quotient of Powers
= a3b5 Simplify.
The quotient is a3b5.
Simplify (
2 a 3 b 5 −
3 b 2
)
3
. Assume
that no denominator equals zero.
( 2 a 3 b 5 − 3 b 2
) 3
= (2 a 3 b 5 ) 3 −
(3 b 2 ) 3 Power of a Quotient
= 2 3 ( a 3 ) 3 ( b 5 ) 3 −
(3 ) 3 ( b 2 ) 3 Power of a Product
= 8 a 9 b 15 − 27 b 6
Power of a Power
= 8 a 9 b 9 − 27
Quotient of Powers
The quotient is 8 a 9 b 9 − 27
.
ExercisesSimplify each expression. Assume that no denominator equals zero.
1. 5 5 − 5 2
2. m 6 − m 4
3. p 5 n 4
− p 2 n
4. a 2 − a 5. x 5 y 3
− x 5 y 2
6. -2 y 7
− 14 y 5
7. x y 6
− y 4 x
8. ( 2 a 2 b − a ) 3
9. ( 4 p 4 r 4
− 3 p 2 r 2
) 3
10. ( 2 r 5 w 3 − r 4 w 3
) 4
11. ( 3 r 6 n 3 − 2 r 5 n
) 4
12. r 7 n 7 t 2 − n 3 r 3 t 2
7-2
Example 1 Example 2
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Chapter 7 12 Glencoe Algebra 1
Study Guide and Intervention (continued)
Division Properties of Exponents
Negative Exponents Any nonzero number raised to the zero power is 1; for example, (-0.5)0 = 1. Any nonzero number raised to a negative power is equal to the reciprocal of the number raised to the opposite power; for example, 6 -3 = 1 −
6 3 . These definitions can be used to
simplify expressions that have negative exponents.
Zero Exponent For any nonzero number a, a0 = 1.
Negative Exponent Property For any nonzero number a and any integer n, a -n = 1 − a n
and 1 −
a -n = a n .
The simplified form of an expression containing negative exponents must contain only positive exponents.
Simplify 4 a -3 b 6 −
16 a 2 b 6 c -5 . Assume that no denominator equals zero.
4 a -3 b 6 − 16 a 2 b 6 c -5
= ( 4 − 16
) ( a -3 − a 2
) ( b 6 − b 6
) ( 1 − c -5
) Group powers with the same base.
= 1 − 4 ( a -3-2 )( b 6-6 )( c 5 ) Quotient of Powers and Negative Exponent Properties
= 1 − 4 a -5 b 0 c 5 Simplify.
= 1 − 4 ( 1 −
a 5 ) (1) c 5 Negative Exponent and Zero Exponent Properties
= c 5 − 4 a 5
Simplify.
The solution is c 5 − 4 a 5
.
ExercisesSimplify each expression. Assume that no denominator equals zero.
1. 2 2 − 2 -3
2. m − m -4
3. p -8
− p 3
4. b -4 − b -5
5. (- x -1 y) 0
− 4 w -1 y 2
6. ( a 2 b 3 ) 2 −
(a b) -2
7. x 4 y 0
− x -2
8. (6 a -1 b) 2 −
( b 2 ) 4 9. (3rt ) 2 u -4
− r -1 t 2 u 7
10. m -3 t -5 − ( m 2 t 3 ) -1
11. ( 4 m 2 n 2 − 8 m -1 �
) 0
12. (-2m n 2 ) -3
− 4 m -6 n 4
7-2
Example
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Chapter 7 13 Glencoe Algebra 1
Skills PracticeDivision Properties of Exponents
Simplify each expression. Assume that no denominator equals zero.
1. 6 5 − 6 4
2. 9 12 − 9 8
3. x 4 − x 2
4. r 3 t 2 − r 3 t 4
5. m − m 3
6. 9 d 7 − 3 d 6
7. 12 n 5 − 36n
8. w 4 x 3 − w 4 x
9. a 3 b 5 − ab 2
10. m 7 p 2
− m 3 p 2
11. -21 w 5 x 2 − 7 w 4 x 5
12. 32 x 3 y 2 z 5
− -8xy z 2
13. ( 4 p 7
− 7 r 2
) 2
14. 4-4
15. 8-2 16. ( 5 − 3 )
-2
17. ( 9 − 11
) -1
18. h 3 − h -6
19. k0(k4)(k-6) 20. k-1(ℓ-6)(m3)
21. f -7
− f 4
22. ( 16 p 5 w 2
− 2 p 3 w 3
) 0
23. f -5 g 4
− h -2
24. 15 x 6 y -9
− 5xy -11
25. -15 t 0 u -1 − 5 u 3
26. 48 x 6 y 7 z 5
− -6x y 5 z 6
7-2
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Chapter 7 14 Glencoe Algebra 1
PracticeDivision Properties of Exponents
Simplify each expression. Assume that no denominator equals zero.
1. 8 8 − 8 4
2. a 4 b 6 − ab 3
3. xy 2
− xy
4. m 5 np
− m 4 p
5. 5 c 2 d 3 − -4 c 2 d
6. 8 y 7 z 6
− 4 y 6 z 5
7. ( 4f 3g −
3 h 6 )
3
8. ( 6 w 5 − 7 p 6 r 3
) 2
9. -4 x 2 − 24 x 5
10. x3(y-5)(x-8) 11. p(q-2)(r-3) 12. 12-2
13. ( 3 − 7 )
-2 14. ( 4 −
3 )
-4 15. 22 r 3 s 2 −
11 r 2 s -3
16. -15 w 0 u -1 − 5 u 3
17. 8 c 3 d 2 f 4
− 4 c -1 d 2 f -3
18. ( x -3 y 5
− 4 -3
) 0
19. 6 f -2 g 3 h 5
− 54 f -2 g -5 h 3
20. -12 t -1 u 5 x -4 − 2 t -3 u x 5
21. r 4 − (3r ) 3
22. m -2 n -5 − ( m 4 n 3 ) -1
23. ( j -1 k 3 ) -4
− j 3 k 3
24. (2 a -2 b ) -3 −
5 a 2 b 4
25. ( q -1 r 3 −
q r -2 )
-5
26. ( 7 c -3 d 3 − c 5 d h -4
) -1
27. ( 2 x 3 y 2 z −
3 x 4 y z -2 )
-2
28. BIOLOGY A lab technician draws a sample of blood. A cubic millimeter of the blood contains 223 white blood cells and 225 red blood cells. What is the ratio of white blood cells to red blood cells?
29. COUNTING The number of three-letter “words” that can be formed with the English alphabet is 263. The number of five-letter “words” that can be formed is 265. How many times more five-letter “words” can be formed than three-letter “words”?
7-2
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Chapter 7 15 Glencoe Algebra 1
Word Problem PracticeDivision Properties of Exponents
1. CHEMISTRY The nucleus of a certain atom is 10-13 centimeters across. If the nucleus of a different atom is 10-11 centimeters across, how many times as large is it as the first atom?
2. SPACE The Moon is approximately 254 kilometers away from Earth on average. The Olympus Mons volcano on Mars stands 25 kilometers high. How many Olympus Mons volcanoes, stacked on top of one another, would fit between the surface of the Earth and the Moon?
3. E-MAIL Spam (also known as junk e-mail) consists of identical messages sent to thousands of e-mail users. People often obtain anti-spam software to filter out the junk e-mail messages they receive. Suppose Yvonne’s anti-spam software filtered out 102 e-mails, and she received 104 e-mails last year. What fraction of her e-mails were filtered out? Write your answer as a monomial.
4. METRIC MEASUREMENT Consider a dust mite that measures 10-3 millimeters in length and a caterpillar that measures 10 centimeters long. How many times as long as the mite is the caterpillar?
5. COMPUTERS In 1995, standard capacity for a personal computer hard drive was 40 megabytes (MB). In 2010, a standard hard drive capacity was 500 gigabytes (GB or Gig). Refer to the table below.
Memory Capacity Approximate Conversions
8 bits = 1 byte
103 bytes = 1 kilobyte
103 kilobytes = 1 megabyte (meg)
103 megabytes = 1 gigabyte (gig)
103 gigabytes = 1 terabyte
103 terabytes = 1 petabyte
a. The newer hard drives have about how many times the capacity of the 1995 drives?
b. Predict the hard drive capacity in the year 2025 if this rate of growth continues.
c. One kilobyte of memory is what fraction of one terabyte?
7-2
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Chapter 7 16 Glencoe Algebra 1
Enrichment
Patterns with PowersUse your calculator, if necessary, to complete each pattern.
a. 210 = b. 510 = c. 410 =
29 = 59 = 49 =
28 = 58 = 48 =
27 = 57 = 47 =
26 = 56 = 46 =
25 = 55 = 45 =
24 = 54 = 44 =
23 = 53 = 43 =
22 = 52 = 42 =
21 = 51 = 41 =
Study the patterns for a, b, and c above. Then answer the questions.
1. Describe the pattern of the exponents from the top of each column to the bottom.
2. Describe the patte rn of the powers from the top of the column to the bottom.
3. What would you expect the following powers to be?
20 50 40
4. Refer to Exercise 3. Write a rule. Test it on patterns that you obtain using 22, 25, and 24 as bases.
Study the pattern below. Then answer the questions.
03 = 0 02 = 0 01 = 0 00 = ? 0-1 does not exist. 0-2 does not exist. 0-3 does not exist.
5. Why do 0-1, 0-2, and 0-3 not exist?
6. Based upon the pattern, can you determine whether 00 exists?
7. The symbol 00 is called an indeterminate, which means that it has no unique value. Thus it does not exist as a unique real number. Why do you think that 00 cannot equal 1?
7-2
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Chapter 7 17 Glencoe Algebra 1
Study Guide and InterventionRational Exponents
Rational Exponents For any real numbers a and b and any positive integer n, if an = b, then a is an nth root of b. Rational exponents can be used to represent nth roots.
Square Root b 1 − 2 = √ � b
Cube Root b 1 − 3 = 3 √ � b
nth Root b 1 − n =
n √ � b
7-3
Write (6xy ) 1 −
2 in radical
form.(6xy )
1 − 2 = √ �� 6xy Defi nition of b
1 −
2
Simplify 625 1 −
4 .
625 1 − 4 = 4 √ �� 625 b
1 − n =
n √ � b
= 4 √ ����� 5 � 5 � 5 � 5 625 = 5 4
= 5 Simplify.
Example 1 Example 2
ExercisesWrite each expression in radical form, or write each radical in exponential form.
1. 14 1 − 2 2. 5 x
1 − 2 3. 17 y
1 − 2
4. 1 2 1 − 2 5. 19 ab
1 − 2 6. √ �� 17
7. √ �� 12n 8. √
��
18b 9. √ �� 37
Simplify.
10. 3 √ �� 343 11. 5 √ �� 1024 12. 51 2 1 − 3
13. 4 √ �� 2401 14. 6 √ ��
64 15. 24 3 1 − 5
16. 3 √ �� 1331 17. 4 √ ���
6561 18. 409 6 1 − 4
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Chapter 7 18 Glencoe Algebra 1
Study Guide and Intervention (continued)
Rational Exponents
7-3
Solve Exponential Equations In an exponential equation, variables occur as exponents. Use the Power Property of Equality and the other properties of exponents to solve exponential equations.
Solve 102 4 x − 1 = 4.
102 4 x − 1 = 4 Original equation
( 4 5 ) x − 1 = 4 Rewrite 1024 as 4 5 .
4 5x − 5 = 4 1 Power of a Power, Distributive Property
5x − 5 = 1 Power Property of Equality
5x = 6 Add 5 to each side.
x = 6 − 5 Divide each side by 5.
ExercisesSolve each equation.
1. 2 x = 128 2. 3 3x + 1 = 81 3. 4 x - 3 = 32
4. 5 x = 15,625 5. 6 3x + 2 = 216 6. 4 5x - 3 = 16
7. 8 x = 4096 8. 9 3x + 3 = 6561 9. 1 1 x - 1 = 1331
10. 3 x = 6561 11. 2 5x + 4 = 512 12. 7 x - 2 = 343
13. 8 x = 262,144 14. 5 5x = 3125 15. 9 2x - 6 = 6561
16. 7 x = 2401 17. 7 3x = 117,649 18. 6 2x - 7 = 7776
19. 9 x = 729 20. 8 3x + 1 = 4096 21. 1 3 3x - 8 = 28,561
Example
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Chapter 7 19 Glencoe Algebra 1
7-3 Skills PracticeRational Exponents
Write each expression in radical form, or write each radical in exponential form.
1. (8 x) 1 − 2 2. 6z
1 − 2 3. √ �� 19
4. √ �� 11 5. 19 x 1 − 2 6. √ �� 34
7. √ �� 27g 8. 33 gh 1 − 2 9. √ ��� 13abc
Simplify.
10. ( 1 − 16
) 1 − 4 11. 5 √ �� 3125 12. 72 9
1 −
3
13. ( 1 − 32
) 1 − 5 14. 6 √ �� 4096 15. 102 4
1 − 5
16. ( 16 − 625
) 1 − 4 17. 6 √ ��� 15,625 18. 117,6 49
1 − 6
Solve each equation.
19. 2 x = 512 20. 3 x = 6561 21. 6 x = 46,656
22. 5 x = 125 23. 3 x - 3 = 243 24. 4 x - 1 = 1024
25. 6 x - 1 = 1296 26. 2 4x + 3 = 2048 27. 3 3x + 3 = 6561
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Chapter 7 20 Glencoe Algebra 1
7-3 PracticeRational Exponents
Write each expression in radical form, or write each radical in exponential form.
1. √ �� 13 2. √ �� 37 3. √ �� 17x
4. (7ab ) 1 −
2 5. 2 1z
1 − 2 6. 13(a b)
1 − 2
Simplify.
7. ( 1 − 81
) 1 − 4 8. 5
√ �� 1024 9. 51 2 1 − 3
10. ( 32 − 1024
) 1 − 5 11. 4
√ �� 1296 12. 312 5 1 − 5
Solve each equation.
13. 3 x = 729 14. 4 x = 4096 15. 5 x = 15,625
16. 6 x + 3 = 7776 17. 3 x - 3 = 2187 18. 4 3x + 4 = 16,384
19. WATER The flow of water F in cubic feet per second over a wier, a small overflow dam,
can be represented by F = 1.26 H 3 − 2 , where H is the height of the water in meters above
the crest of the wier. Find the height of the water if the flow of the water is 10.08 cubic feet per second.
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Chapter 7 21 Glencoe Algebra 1
7-3 Word Problem PracticeRational Exponents
1. VELOCITY The velocity v in feet per second of a freely falling object that has fallen h feet can be represented by
v = 8 h 1 − 2 . Find the distance that an object
has fallen if its velocity is 96 feet per second.
2. ELECTRICITY The relationship of the current, the power, and the resistance in an appliance can be modeled by
I R 1 − 2 = √ � P , where I is the current in
amperes, P is the power in watts, and R is the resistance in ohms. Find the power that an appliance is using if the current is 2.5 amps and the resistance is 16 ohms.
3. GEOMETRY The surface area T of a cube in square inches can be determined
by T = 6 V 2 − 3 , where V is the volume of
the cube in cubic inches.
a. Find the surface area of a cube that has a volume of 4096 cubic inches.
b. Find the volume of a cube that has a surface area of 96 square inches.
4. PLANETS The average distance d in astronomical units that a planet is from
the Sun can be modeled by d = t 2 − 3 , where
t is the number of Earth years that it takes for the planet to orbit the Sun.
a. Find the average distance a planet is from the Sun if the planet has an orbit of 27 Earth years.
b. Find the time that it would take a planet to orbit the Sun if its average distance from the Sun is 4 astronomical units.
5. BIOLOGY The relationship between the mass m in kilograms of an organism and its metabolism P in Calories per day can
be represented by P = 73.3 4 √ �� m 3 . Find
the mass of an organism that has a metabolism of 586.4 Calories per day.
6. MANUFACTURING The profit P of a company in thousands of dollars can be
modeled by P = 12.75 5 √ � c 2 , where c is the
number of customers in hundreds. If the profit of the company is $51,000, how many customers do they have?
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Chapter 7 22 Glencoe Algebra 1
Enrichment7-3
CounterexamplesSome statements in mathematics can be proven false by counterexamples. Consider the following statement.For any numbers a and b, a - b = b - a.You can prove that this statement is false in general if you can find one example for which the statement is false.Let a = 7 and b = 3. Substitute these values in the equation above.
7 - 3 � 3 - 7 4 ≠ -4
In general, for any numbers a and b, the statement a - b = b - a is false. You can make the equivalent verbal statement: subtraction is not a commutative operation.
In each of the following exercises a, b, and c are any numbers. Prove that the statement is false by counterexample.
1. a - (b - c) � (a - b) - c 2. a ÷ (b ÷ c) � (a ÷ b) ÷ c
3. a ÷ b � b ÷ a 4. a ÷ (b + c) � (a ÷ b) + (a ÷ c)
5. a 1 − 2 + a
1 −
2 � a 1 6. a c � b d � (ab ) c + d
7. Write the verbal equivalents for Exercises 1, 2, and 3.
8. For the Distributive Property a(b + c) = ab + ac, it is said that multiplication distributes over addition. Exercise 4 proves that some operations do not distribute. Write a statement for the exercise that indicates this.
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Chapter 7 23 Glencoe Algebra 1
Study Guide and InterventionScientifi c Notation
7-4
Scientific Notation Very large and very small numbers are often best represented using a method known as scientific notation. Numbers written in scientific notation take the form a × 10n, where 1 ≤ a < 10 and n is an integer. Any number can be written in scientific notation.
Express 34,020,000,000 in scientific notation.Step 1 Move the decimal point until it is to the right of the first nonzero digit. The result is a real number a. Here, a = 3.402.
Step 2 Note the number of places n and the direction that you moved the decimal point. The decimal point moved 10 places to the left, so n = 10.
Step 3 Because the decimal moved to the left, write the number as a × 10n.34,020,000,000 = 3.4020000000 × 1010
Step 4 Remove the extra zeros. 3.402 × 1010
Express 4.11 × 10-6 in standard notation.Step 1 The exponent is –6, so n = –6.
Step 2 Because n < 0, move the decimal point 6 places to the left. 4.11 × 10-6 ⇒ .00000411
Step 3 4.11 × 10-6 ⇒ 0.00000411Rewrite; insert a 0 before the decimal point.
Example 1 Example 2
ExercisesExpress each number in scientific notation.
1. 5,100,000 2. 80,300,000,000 3. 14,250,000
4. 68,070,000,000,000 5. 14,000 6. 901,050,000,000
7. 0.0049 8. 0.000301 9. 0.0000000519
10. 0.000000185 11. 0.002002 12. 0.00000771
Express each number in standard form.
13. 4.91 × 104 14. 3.2 × 10-5 15. 6.03 × 108
16. 2.001 × 10-6 17. 1.00024 × 1010 18. 5 × 105
19. 9.09 × 10-5 20. 3.5 × 10-2 21. 1.7087 × 107
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Chapter 7 24 Glencoe Algebra 1
Study Guide and Intervention (continued)
Scientifi c Notation
7-4
Products and Quotients in Scientific Notation You can use scientific notation to simplify multiplying and dividing very large and very small numbers.
Evaluate (9.2 × 10-3) ×(4 × 108). Express the result in both scientific notation and standard form.
(9.2 × 10-3)(4 × 108) Original expression
= (9.2 × 4)(10-3 × 108) Commutative andAssociative Properties
= 36.8 × 105 Product of Powers
= (3.68 × 101) × 105 36.8 = 3.68 × 10
= 3.68 × 106 Product of Powers
= 3,680,000 Standard Form
Evaluate (2.76 × 10
7
)
−
(6.9 × 10
5
)
.
Express the result in both scientific notation and standard form. (2.76 × 10 7 )
− (6.9 × 10 5 )
= ( 2.76 − 6.9
) ( 10 7 −
10 5 ) Product rule for
fractions
= 0.4 × 102 Quotient of Powers
= 4.0 × 10-1 × 102 0.4 = 4.0 × 10-1
= 4.0 × 101 Product of Powers
= 40 Standard form
Example 1 Example 2
ExercisesEvaluate each product. Express the results in both scientific notation and standard form.
1. (3.4 × 103)(5 × 104) 2. (2.8 × 10-4)(1.9 × 107)
3. (6.7 × 10-7)(3 × 103) 4. (8.1 × 105)(2.3 × 10-3)
5. (1.2 × 1 0 -4 ) 2 6. (5.9 × 1 0 5 ) 2
Evaluate each quotient. Express the results in both scientific notation and standard form.
7. (4.9 × 1 0 -3 )
− (2.5 × 1 0 -4 )
8. 5.8 × 10 4 − 5 × 10 -2
9. (1.6 × 1 0 5 )
− (4 × 1 0 -4 )
10. 8.6 × 10 6 − 1.6 × 10 -3
11. (4.2 × 1 0 -2 )
− (6 × 1 0 -7 )
12. 8.1 × 10 5 − 2.7 × 10 4
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Chapter 7 25 Glencoe Algebra 1
Skills PracticeScientifi c Notation
7-4
Express each number in scientific notation.
1. 3,400,000,000 2. 0.000000312
3. 2,091,000 4. 980,200,000,000,000
5. 0.00000000008 6. 0.00142
Express each number in standard form.
7. 2.1 × 105 8. 8.023 × 10-7
9. 3.63 × 10-6 10. 7.15 × 108
11. 1.86 × 10-4 12. 4.9 × 105
Evaluate each product. Express the results in both scientific notation and standard form.
13. (6.1 × 105)(2 × 105) 14. (4.4 × 106)(1.6 × 10-9)
15. (8.8 × 108)(3.5 × 10-13) 16. (1.35 × 108)(7.2 × 10-4)
17. (2.2 × 1 0 -3 ) 2 18. (3.4 × 1 0 2 ) 2
Evaluate each quotient. Express the results in both scientific notation and standard form.
19. (9.2 × 10-8) −
(2 × 10-6) 20. (4.8 × 104)
− (3 × 10-5)
21. (1.161 × 10-9) −
(4.3 × 10-6) 22.
(4.625 × 1 0 10 ) −
(1.25 × 10 4 )
23. (2.376 × 10-4) −
(7.2 × 10-8) 24. (8.74 × 10-3)
− (1.9 × 105)
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Chapter 7 26 Glencoe Algebra 1
PracticeScientifi c Notation
7-4
Express each number in scientific notation.
1. 1,900,000 2. 0.000704
3. 50,040,000,000 4. 0.0000000661
Express each number in standard form.
5. 5.3 × 107 6. 1.09 × 10-4
7. 9.13 × 103 8. 7.902 × 10-6
Evaluate each product. Express the results in both scientific notation and standard form.
9. (4.8 × 104)(6 × 106) 10. (7.5 × 10-5)(3.2 × 107)
11. (2.06 × 104)(5.5 × 10-9) 12. (8.1 × 10-6)(1.96 × 1011)
13. (7.2 × 1 0 -5 ) 2 14. (5.29 × 1 0 6 ) 2
Evaluate each quotient. Express the results in both scientific notation and standard form.
15. (4.2 × 1 0 5 ) −
(3 × 1 0 -3 ) 16. (1.76 × 1 0 -11 )
− (2.2 × 1 0 -5 )
17. (7.05 × 1 0 12 ) −
(9.4 × 1 0 7 ) 18. (2.04 × 1 0 -4 )
− (3.4 × 1 0 5 )
19. GRAVITATION Issac Newton’s theory of universal gravitation states that the equation F = G
m1m2 − r2
can be used to calculate the amount of gravitational force in newtons
between two point masses m1 and m2 separated by a distance r. G is a constant equal to 6.67 × 10-11 Nm2kg–2. The mass of Earth m1 is equal to 5.97 × 1024 kg, the mass of the Moon m2 is equal to 7.36 × 1022 kg, and the distance r between the two is 384,000,000 m.
a. Express the distance r in scientific notation.
b. Compute the amount of gravitational force between Earth and the Moon. Express your answer in scientific notation.
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Chapter 7 27 Glencoe Algebra 1
Word Problem PracticeScientifi c Notation
7-4
1. PLANETS Neptune’s mean distance from the Sun is 4,500,000,000 kilometers. Uranus’ mean distance from the Sun is 2,870,000,000 kilometers. Express these distances in scientific notation.
2. PATHOLOGY The common cold is caused by the rhinovirus, which commonly measures 2 × 10-8 m in diameter. The E. coli bacterium, which causes food poisoning, commonly measures 3 × 10-6 m in length. Express these measurements in standard form.
3. COMMERCIALS A 30-second commercial aired during the 2007 Super Bowl cost $2,600,000. A 30-second commercial aired during the 1967 Super Bowl cost $40,000. Express these values in scientific notation. How many times more expensive was it to air an advertisement during the 2007 Super Bowl than the 1967 Super Bowl?
4. AVOGADRO’S NUMBER Avogadro’s number is an important concept in chemistry. It states that the number 6.022 × 1023 is approximately equal to the number of molecules in 12 grams of carbon 12. Use Avogadro’s number to determine the number of molecules in 5 × 10-7 grams of carbon 12.
5. COAL RESERVES The table below shows the number of kilograms of coal select countries had in proven reserve at the end of a recent year.
Coal Reserves
Country Coal (kg)
United States 2.46 × 1014
Russia 1.57 × 1014
India 9.24 × 1013
Romania 4.94 × 1011
Source: British Petroleum
a. Express each country’s coal reserves in standard form.
b. How many times more coal does the United States have than Romania?
c. One kilogram of coal has an energy density of 2.4 × 107 joules. What is the total energy density of the United States’ coal reserve? Express your answer in scientific notation.
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Chapter 7 28 Glencoe Algebra 1
7-4 EnrichmentEngineering Notation
Engineering notation is a variation on scientific notation where numbers are expressed as powers of 1000 rather than as powers of 10. Engineering notation takes the familiar form of a × 10n, but n is restricted to multiples of three and 1 ≤ |a|< 1000.One advantage to engineering notation is that numbers can be neatly expressed using SI prefixes. These prefixes are typically used for scientific measurements.
1000n 10n SI Prefi x Symbol
10005 1015 peta P
10004 1012 tera T
10003 109 giga G
10002 106 mega M
10001 103 kilo k
1000-1 10-3 milli m
1000-2 10-6 micro μ
1000-3 10-9 nano n
1000-4 10-12 pico p
1000-5 10-15 femto f
NUCLEAR POWER The output of a nuclear power plant is measured to be 620,000,000 watts. Express this number in engineering notation and using SI prefixes.
To express a number in engineering notation, first convert the number to scientific notation.
Step 1 620,000,000 ⇒ 6.20000000 a = 6.20000000
Step 2 The decimal point moved 8 places to the left, so n = 8.
Step 3 620,000,000 = 6.20000000 × 108 = 6.2 × 108
Because 8 is not a multiple of 3, we need to round down n to the next multiple of 3.
Step 4 6.2 × 108 = (6.2 × 102) × 106 620 = 6.2 × 102
Step 5 = 620 × 106 Product of Powers
The output of the power plant is 620 × 106 watts. Using the chart above, the prefix for 106 is found to be mega, or M. The output of the power plant is 620 megawatts, or 620MW.
ExercisesExpress each number in engineering notation.
1. 40,000,000,000 2. 180,000,000,000,000
3. 0.00006 4. 0.00000000000039
Express each measurement using SI prefixes.
5. 0.00000000014 gram 6. 40,000,000,000 watts
7. 63,100,000,000,000 bytes 8. 0.0000002 meter
Example
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Chapter 7 29 Glencoe Algebra 1
7-5
Graph Exponential FunctionsExponential Function a function defi ned by an equation of the form y = a bx, where a ≠ 0, b > 0, and b ≠ 1
You can use values of x to find ordered pairs that satisfy an exponential function. Then you can use the ordered pairs to graph the function.
Graph y = 3x. Find the y-intercept and state the domain and range.
x y
-2 1 −
9
-1 1 −
3
0 1
1 3
2 9
The y-intercept is 1. The domain is all real numbers, and the range is all positive numbers.
x
y
O
Graph y = (
1 −
4 )
x
. Find the y-intercept and state the domain and range.
The y-intercept is 1. The domain is all real numbers, and the range is all positive numbers.
x
y
O 2
8
ExercisesGraph each function. Find the y-intercept and state the domain and range.
1. y = 0.3x 2. y = 3x + 1 3. y = ( 1 − 3 )
x
+ 1
x
y
O 1
2
x
y
O 2
16
4
8
12
x
y
O 1
2
Example 1 Example 2
x y
-2 16
-1 4
0 1
1 1 −
4
2 1 −
16
Study Guide and InterventionExponential Functions
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Chapter 7 30 Glencoe Algebra 1
7-5 Study Guide and Intervention (continued)
Exponential Functions
Identify Exponential Behavior It is sometimes useful to know if a set of data is exponential. One way to tell is to observe the shape of the graph. Another way is to observe the pattern in the set of data.
Determine whether the set of data shown below displays exponential behavior. Write yes or no. Explain why or why not.
Method 1: Look for a PatternThe domain values increase by regular intervals of 2, while the range values have a common factor of 1 −
2 . Since the domain
values increase by regular intervals and the range values have a common factor, the data are probably exponential.
Method 2: Graph the Data The graph shows
rapidly decreasing values of y as x increases. This is characteristic of exponential behavior.
Exercises
Determine whether the set of data shown below displays exponential behavior. Write yes or no. Explain why or why not.
1. x 0 1 2 3
y 5 10 15 20
2. x 0 1 2 3
y 3 9 27 81
3. x -1 1 3 5
y 32 16 8 4
4. x -1 0 1 2 3
y 3 3 3 3 3
5. x -5 0 5 10
y 1 0.5 0.25 0.125
6. x 0 1 2 3 4
y 1 − 3 1 −
9 1 −
27 1 −
81 1
− 243
Example
x 0 2 4 6 8 10
y 64 32 16 8 4 2
x
y
O 4 8
16
32
48
72
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Chapter 7 31 Glencoe Algebra 1
7-5 Skills PracticeExponential Functions
Graph each function. Find the y-intercept, and state the domain and range.
1. y = 2x 2. y = ( 1 − 3 )
x
3. y = 3(2x) 4. y = 3x + 2
Determine whether the set of data shown below displays exponential behavior. Write yes or no. Explain why or why not.
5. x -3 -2 -1 0
y 9 12 15 18
6. x 0 5 10 15
y 20 10 5 2.5
7. x 4 8 12 16
y 20 40 80 160
8. x 50 30 10 -10
y 90 70 50 30
x
y
Ox
y
O
x
y
Ox
y
O
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Chapter 7 32 Glencoe Algebra 1
7-5 Practice Exponential Functions
Graph each function. Find the y-intercept and state the domain and range.
1. y = ( 1 − 10
) x
2. y = 3x 3. y = ( 1 − 4 )
x
4. y = 4(2x) + 1 5. y = 2(2x - 1) 6. y = 0.5(3x - 3)
Determine whether the set of data shown below displays exponential behavior. Write yes or no. Explain why or why not.
7. x 2 5 8 11
y 480 120 30 7.5
8. x 21 18 15 12
y 30 23 16 9
9. LEARNING Ms. Klemperer told her English class that each week students tend to forget one sixth of the vocabulary words they learned the previous week. Suppose a student learns 60 words. The number of words remembered can be described by the function
W(x) = 60 ( 5 − 6 )
x
, where x is the number of weeks that pass. How many words will the student remember after 3 weeks?
10. BIOLOGY Suppose a certain cell reproduces itself in four hours. If a lab researcher begins with 50 cells, how many cells will there be after one day, two days, and three days? (Hint: Use the exponential function y = 50(2x).)
x
y
Ox
y
O
x
y
O
x
y
Ox
y
Ox
y
O
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Chapter 7 33 Glencoe Algebra 1
7-5
1. WASTE Suppose the waste generated by nonrecycled paper and cardboard products is approximated by the following function.
y = 1000(2)0.3x
Sketch the exponential function on the coordinate grid below.
y
xO
950650350
18501550
24502150
1250
4321-2-1-3-4
2. MONEY Tatyana’s grandfather gave her one penny on the day she was born. He plans to double the amount he gives her every day. Estimate how much she will receive from her grandfather on the 12th day of her life.
3. PICTURE FRAMESSince a picture frame includes a border, the picture must be smaller in area than the entire frame. The table shows the relationship between picture area and frame length for a particular line of frames. Is this an exponential relationship? Explain.
4. DEPRECIATION The value of Royce Company’s computer equipment is decreasing in value according to the following function.
y = 4000(0.87)x
In the equation, x is the number of years that have elapsed since the equipment was purchased and y is the value in dollars. What was the value 5 years after it was purchased? Round your answer to the nearest dollar.
5. METEOROLOGY The atmospheric pressure in millibars at altitude x meters can be approximated by the following function. The function is valid for values of x between 0 and 10,000.
f (x) = 1038(1.000134)-x
a. What is the pressure at sea level?
b. The McDonald Observatory in Texas is at an altitude of 2000 meters. What is the approximate atmospheric pressure there?
c. As altitude increases, what happens to atmospheric pressure?
Word Problem PracticeExponential Functions
Side Picture
Length Area
(in.) (in2)
5 6
6 12
7 20
8 30
9 42
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Chapter 7 34 Glencoe Algebra 1
EnrichmentLogarithmic Functions
7-5
You have found the inverse of a linear function by interchanging x and y in the equation of the function. The inverse of an exponential function is called a logarithmic function.
Find the inverse function of the exponential function y = 2x. Make a table of values for each function. Then graph both functions.
To find the inverse function, interchange x and y. The inverse of y = 2 x is x = 2 y .
y = 2 x x = 2 y
x y x y
-3 1 − 8 1 −
8 -3
-2 1 − 4 1 −
4 -2
-1 1 − 2 1 −
2 -1
0 1 1 0
1 2 2 1
2 4 4 2
3 8 8 3
In general the inverse of y = b x is x = b y . In x = b y , the variable y is called the logarithm of x. This is usually written as y = lo g b x.
Exercises
1. What are the domain and range of y = lo g 2 x? How are the domain and range related to the domain and range of y = 2 x ?
2. How are the graphs of y = lo g 2 x and y = 2 x related?
3. Through which quadrants do the graphs of y = lo g 2 x and y = 2 x pass?
4. If an exponential function finds population as a function of time, what can you conclude about its inverse logarithmic function?
5. RESEARCH Investigate real-world uses of logarithmic functions. How are logarithmic functions used to model real-world situations?
Example
y
xO
12
8 12
8
4
4
y = x
y = 2x
x = 2y
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Chapter 7 35 Glencoe Algebra 1
7-6 Study Guide and InterventionGrowth and Decay
Exponential Growth Population increases and growth of monetary investments are examples of exponential growth. This means that an initial amount increases at a steady rate over time.
The general equation for exponential growth is y = a(1 + r )t.
• y represents the fi nal amount.
Exponential Growth • a represents the initial amount.
• r represents the rate of change expressed as a decimal.
• t represents time.
POPULATION The population of Johnson City in 2005 was 25,000. Since then, the population has grown at an average rate of 3.2% each year.
a. Write an equation to represent the population of Johnson City since 2005.
The rate 3.2% can be written as 0.032.y = a(1 + r)t
y = 25,000(1 + 0.032)t
y = 25,000(1.032)t
b. According to the equation, what will the population of Johnson City be in 2015?
In 2015 t will equal 2015 - 2005 or 10.Substitute 10 for t in the equation from part a.y = 25,000(1.032)10 t = 10
≈ 34,256In 2015 the population of Johnson City will be about 34,256.
INVESTMENT The Garcias have $12,000 in a savings account. The bank pays 3.5% interest on savings accounts, compounded monthly. Find the balance in 3 years.
The rate 3.5% can be written as 0.035. The special equation for compound interest is A = P (1 + r−n)
nt, where A
represents the balance, P is the initial amount, r represents the annual rate expressed as a decimal, n represents the number of times the interest is compounded each year, and t represents the number of years the money is invested.
A = P (1 + r−n)nt
= 12,000 (1 + 0.035−12 )
3(12)
≈ 13,326.49In three years, the balance of the account will be $13,326.49.
Exercises 1. POPULATION The population of the United 2. INVESTMENT Determine the
States has been increasing at an average value of an investment of $2500 annual rate of 0.91%. If the population was if it is invested at an interest rate of about 303,146,000 in 2008, predict the 5.25% compounded monthly for population in 2012. 4 years.
3. POPULATION It is estimated that the 4. INVESTMENT Determine the population of the world is increasing at value of an investment of $100,000 an average annual rate of 1.3%. If the if it is invested at an interest rate of 2008 population was about 6,641,000,000, 5.2% compounded quarterly for predict the 2015 population. 12 years.
Example 1 Example 2
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Chapter 7 36 Glencoe Algebra 1
7-6 Study Guide and Intervention (continued)
Growth and Decay
Exponential Decay Radioactive decay and depreciation are examples of exponential decay. This means that an initial amount decreases at a steady rate over a period of time.
The general equation for exponential decay is y = a(1 - r)t .
• y represents the fi nal amount.
Exponential Decay • a represents the initial amount.
• r represents the rate of decay expressed as a decimal.
• t represents time.
DEPRECIATION The original price of a tractor was $45,000. The value of the tractor decreases at a steady rate of 12% per year.
a. Write an equation to represent the value of the tractor since it was purchased.
The rate 12% can be written as 0.12.y = a(1 - r)t General equation for exponential decay
y = 45,000(1 - 0.12)t a = 45,000 and r = 0.12
y = 45,000(0.88)t Simplify.
b. What is the value of the tractor in 5 years?
y = 45,000(0.88)t Equation for decay from part a
y = 45,000(0.88)5 t = 5
y ≈ 23,747.94 Use a calculator.
In 5 years, the tractor will be worth about $23,747.94.
Exercises 1. POPULATION The population of Bulgaria has been decreasing at an annual
rate of 0.89%. If the population of Bulgaria was about 7,450,349 in the year 2005, predict its population in the year 2015.
2. DEPRECIATION Mr. Gossell is a machinist. He bought some new machinery for about $125,000. He wants to calculate the value of the machinery over the next 10 years for tax purposes. If the machinery depreciates at the rate of 15% per year, what is the value of the machinery (to the nearest $100) at the end of 10 years?
3. ARCHAEOLOGY The half-life of a radioactive element is defined as the time that it takes for one-half a quantity of the element to decay. Radioactive carbon-14 is found in all living organisms and has a half-life of 5730 years. Consider a living organism with an original concentration of carbon-14 of 100 grams.
a. If the organism lived 5730 years ago, what is the concentration of carbon-14 today?
b. If the organism lived 11,460 years ago, determine the concentration of carbon-14 today.
4. DEPRECIATION A new car costs $32,000. It is expected to depreciate 12% each year for 4 years and then depreciate 8% each year thereafter. Find the value of the car in 6 years.
Example
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Chapter 7 37 Glencoe Algebra 1
7-6 Skills PracticeGrowth and Decay
1. POPULATION The population of New York City increased from 8,008,278 in 2000 to 8,168,388 in 2005. The annual rate of population increase for the period was about 0.4%.
a. Write an equation for the population t years after 2000.
b. Use the equation to predict the population of New York City in 2015.
2. SAVINGS The Fresh and Green Company has a savings plan for its employees. If an employee makes an initial contribution of $1000, the company pays 8% interest compounded quarterly.
a. If an employee participating in the plan withdraws the balance of the account after 5 years, how much will be in the account?
b. If an employee participating in the plan withdraws the balance of the account after 35 years, how much will be in the account?
3. HOUSING Mr. and Mrs. Boyce bought a house for $96,000 in 1995. The real estate broker indicated that houses in their area were appreciating at an average annual rate of 7%. If the appreciation remained steady at this rate, what was the value of the Boyce’s home in 2009?
4. MANUFACTURING Zeller Industries bought a piece of weaving equipment for $60,000. It is expected to depreciate at an average rate of 10% per year.
a. Write an equation for the value of the piece of equipment after t years.
b. Find the value of the piece of equipment after 6 years.
5. FINANCES Kyle saved $500 from a summer job. He plans to spend 10% of his savings each week on various forms of entertainment. At this rate, how much will Kyle have left after 15 weeks?
6. TRANSPORTATION Tiffany’s mother bought a car for $9000 five years ago. She wants to sell it to Tiffany based on a 15% annual rate of depreciation. At this rate, how much will Tiffany pay for the car?
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Chapter 7 38 Glencoe Algebra 1
7-6 Practice Growth and Decay
1. COMMUNICATIONS Sports radio stations numbered 220 in 1996. The number of sports radio stations has since increased by approximately 14.3% per year.
a. Write an equation for the number of sports radio stations for t years after 1996.
b. If the trend continues, predict the number of sports radio stations in 2015.
2. INVESTMENTS Determine the amount of an investment if $500 is invested at an interest rate of 4.25% compounded quarterly for 12 years.
3. INVESTMENTS Determine the amount of an investment if $300 is invested at an interest rate of 6.75% compounded semiannually for 20 years.
4. HOUSING The Greens bought a condominium for $110,000 in 2010. If its value appreciates at an average rate of 6% per year, what will the value be in 2015?
5. DEFORESTATION During the 1990s, the forested area of Guatemala decreased at an average rate of 1.7%.
a. If the forested area in Guatemala in 1990 was about 34,400 square kilometers, write an equation for the forested area for t years after 1990.
b. If this trend continues, predict the forested area in 2015.
6. BUSINESS A piece of machinery valued at $25,000 depreciates at a steady rate of 10% yearly. What will the value of the piece of machinery be after 7 years?
7. TRANSPORTATION A new car costs $18,000. It is expected to depreciate at an average rate of 12% per year. Find the value of the car in 8 years.
8. POPULATION The population of Osaka, Japan, declined at an average annual rate of 0.05% for the five years between 1995 and 2000. If the population of Osaka was 11,013,000 in 2000 and it continues to decline at the same rate, predict the population in 2050.
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Chapter 7 39 Glencoe Algebra 1
7-6
1. DEPRECIATION The value of a new plasma television depreciates by about 7% each year. Aeryn purchases a 50-inch plasma television for $3000. What is its value after 4 years? Round your answer to the nearest hundred.
2. MONEY Hans opens a savings account by depositing $1200 in an account that earns 3 percent interest compounded weekly. How much will his investment be worth in 10 years? Assume that there are exactly 52 weeks in a year and round your answer to the nearest cent.
3. HIGHER EDUCATION The table lists the average costs of attending a four-year college in the United States during a recent year.
Source: College Board
Russ’s parents invested money in a savings account earning an average of 4.5 percent interest, compounded monthly. After 15 years, they have exactly the right amount to cover the tuition, fees, room and board for Russ’s first year at a public college. What was their initial investment? Round your answer to the nearest dollar.
4. POPULATION In 2007 the U.S. Census Bureau estimated the population of the United States estimated at 301 million. The annual rate of growth is about 0.89%. At this rate, what is the expected population at the time of the 2020 census? Round your answer to the nearest ten million.
5. MEDICINE When doctors prescribe medication, they have to consider the rate at which the body filters a drug from the bloodstream. Suppose it takes the human body 6 days to filter out half of the Flu-B-Gone vaccine. The amount of Flu-B-Gone vaccine remaining in the bloodstream x days after an injection is
given by the equation y = y0 (0.5) x − 6 , where
y0 is the initial amount. Suppose a doctor injects a patient with 20 μg (micrograms) of Flu-B-Gone.
a. How much of the vaccine will remain after 1 day? Round your answer to the nearest tenth.
b. How much of the vaccine will remain after 12 days? Round your answer to the nearest tenth.
c. After how many days will the amount of vaccine be less than 1 μg?
Word Problem PracticeGrowth and Decay
College
Sector
Tuition and
Fees
Room and
Board
Four-year
Public$5941 $6636
Four-year
Private $21,235 $7,791
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Chapter 7 40 Glencoe Algebra 1
7-6
You can use the formula for compound interest A = P (1 + r − n ) nt when n, the number of times
a year interest is compounded, is known. A special type of compound interest calculation regularly used in finance is continuously compounded interest, where n approaches infinity.
INVESTING Mr. Rivera placed $5000 in an investment account that has an interest rate of 9.5% per year.
Exercises
1. SAVINGS Mr. Harris saves $20,000 in a money-market account at a rate of 5.2%.
a. Determine the value of his investment after 10 years if interest iscompounded quarterly.
b. Determine the value of his investment after 10 years if interest iscompounded continuously.
2. COLLEGE SAVINGS Shannon is choosing between two different savings accounts for her college fund. The first account compounds interest semiannually at a rate of 11.0%. The second account compounds interest continuously at a rate of 10.8%. If Shannon plans to keep her money in the account for 5 years, which account should she choose? Explain.
EnrichmentContinuously Compounding Interest
General formula: A = Pert
A = current amount of investment
P = initial amount of investment
e = natural logarithm, a constant approximately equal to 2.71828
r = annual rate of interest, expressed as a decimal
t = number of years the money is invested
Example
a. How much money will be in the account after 5 years if interest is compounded monthly?
A = P (1 + r − n ) nt
Compound interest
equation
= 5000 (1 + 0.095 − 12
) 12(5)
P = 5000, r = 0.095,
n = 12, and t = 5
= 5000(1.0079)60 Simplify.
= 8025.05 Use a calculator.
There will be about $8025.05 in the account if interest is compounded monthly.
b. How much money will be in the account after 5 years if interest is compounded continuously?
A = Pert Continuous interest
equation
= 5000(2.71828)0.095(5) P = 5000, e = 2.71828,
r = 0.095, and t = 5
= 5000(2.71828)0.475 Simplify.
= 8040.07 Use a calculator.
There will be about $8040.07 in the account if interest is compounded continuously.
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Chapter 7 41 Glencoe Algebra 1
7-6 Spreadsheet ActivityCompound Interest
Exercises
Use the spreadsheet of accounts involving compound interest.
1. How are the doubling times affected if the accounts compound interest quarterly instead of monthly?
2. How long will it take each account to reach $4000 if the interest is compounded monthly? quarterly?
3. How do the interest rate and the number of times the interest is compounded affect the growth of an investment?
Banks often use spreadsheets to calculate and store financial data. One application is to calculate compound interest on an account.
Use a spreadsheet to find the time it will take an investment of $1000 to double. Suppose you can choose from investments that have annual interest rates of 5%, 8%, or 10% compounded monthly.The compound interest equation is A = P (1 + r − n )
nt , where P is the principal or initial
investment, A is the final amount of the investment, r is the annual interest rate, n is the number of times interest is paid, or compounded, each year, and t is the number of years. In this case, P = 1000 and n = 12.
Step 1 Use Column A of the spreadsheet for the years.
Step 2 Columns B, C, and D contain the formulas for the final amounts of the investments. Format the cells in these columns as currency so that the amounts are shown in dollars and cents. Each formula will use the values in Column A as the value of t. For example, the formula that is in cell C3 is =1000*(1 + (0.08/12))^(12 * A3).
Study the spreadsheet for the times when each investment exceeds $2000. At 5%, the $1000 will double in 14 years, at 8% it will double in 9 years, and at 10% it will double in 7 years.
A1
3456789
1011
2
B C D
1213141516
Years$1,051.16
$1,104.94
$1,161.47
$1,220.90
$1,283.36
$1,349.02
$1,418.04
$1,490.59
$1,566.85
$1,647.01
$1,731.27
$1,819.85
$1,912.96
$2,010.83
5% 8% 10%$1,083.00
$1,172.89
$1,270.24
$1,375.67
$1,489.85
$1,613.50
$1,747.42
$1,892.46
$2,049.53
$2,219.64
$2,403.87
$2,603.39
$2,819.47
$3,053.48
$1,104.71
$1,220.39
$1,348.18
$1,489.35
$1,645.30
$1,817.59
$2,007.92
$2,218.18
$2,450.45
$2,707.04
$2,990.50
$3,303.65
$3,649.58
$4,031.74
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Sheet 1 Sheet 2 Sheet 3
Example
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Chapter 7 42 Glencoe Algebra 1
7-7
Recognize Geometric Sequences A geometric sequence is a sequence in which each term after the first is found by multiplying the previous term by a nonzero constant r called the common ratio. The common ratio can be found by dividing any term by its previous term.
Exercises
Determine whether each sequence is arithmetic, geometric, or neither. Explain.
1. 1, 2, 4, 8, . . . 2. 9, 14, 6, 11, . . .
3. 2 − 3 , 1 −
3 , 1 −
6 , 1 −
12 , . . . 4. –2, 5, 12, 19, . . .
Find the next three terms in each geometric sequence.
5. 648, –216, 72, . . . 6. 25, –5, 1, . . .
7. 1 − 16
, 1 − 2 , 4, . . . 8. 72, 36, 18, . . .
Study Guide and InterventionGeometric Sequences as Exponential Functions
Example 1 Determine whether the sequence is arithmetic, geometric, or neither: 21, 63, 189, 567, . . .
Find the ratios of the consecutive terms. If the ratios are constant, the sequence is geometric.21 63 189 567
63 − 21
= 189 − 63
= 567 − 189
= 3
Because the ratios are constant, the sequence is geometric. The common ratio is 3.
Find the next three terms in this geometric sequence:-1215, 405, -135, 45, . . .
Step 1 Find the common ratio.–1215 405 –135 45
405 − -1215
= -135 − 405
= 45 − -135
= - 1 − 3
The value of r is - 1 − 3 .
Step 2 Multiply each term by the common ratio to find the next three terms.
45 –15 5 - 5 − 3
× (-
1 − 3 ) × (-
1 −
3 ) × (-
1 − 3 )
The next three terms of the sequence are –15, 5, and - 5 −
3 .
Example 2
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Chapter 7 43 Glencoe Algebra 1
7-7
Geometric Sequences and Functions The nth term an of a geometric sequence with first term a1 and common ratio r is given by the following formula, where n is any positive integer: an = a1 · r
n – 1.
Exercises
1. Write an equation for the nth term of the geometric sequence –2, 10, –50, . . . . Find the eleventh term of this sequence.
2. Write an equation for the nth term of the geometric sequence 512, 128, 32, . . . . Find the sixth term of this sequence.
3. Write an equation for the nth term of the geometric sequence 4 − 9 , 4, 36, . . . .
Find the eighth term of this sequence.
4. Write an equation for the nth term of the geometric sequence 6, –54, 486, . . . . Find the ninth term of this sequence.
5. Write an equation for the nth term of the geometric sequence 100, 80, 64, . . . . Find the seventh term of this sequence.
6. Write an equation for the nth term of the geometric sequence 2 − 5 , 1 −
10 , 1 −
40 , . . . .
Find the sixth term of this sequence.
7. Write an equation for the nth term of the geometric sequence 3 − 8 , - 3 −
2 , 6, . . . .
Find the tenth term of this sequence.
8. Write an equation for the nth term of the geometric sequence –3, –21, –147, . . . . Find the fifth term of this sequence.
Study Guide and Intervention (continued)
Geometric Sequences as Exponential Functions
Example a. Write an equation for the nth term of the geometric sequence 5, 20, 80, 320, . . .
The first term of the sequence is 320. So, a1 = 320. Now find the common ratio.5 20 80 320
20 − 5 = 80 −
20 = 320 −
80 = 4
The common ratio is 4. So, r = 4.an = a1 · r
n – 1 Formula for nth term
an = 5 · 4n – 1 a1 = 5 and r = 4
b. Find the seventh term of this sequence.
Because we are looking for the seventh term, n = 7.an = a1 · r
n – 1 Formula for nth term
a7 = 5 · 47 – 1 n = 7
= 5 · 46 Simplify.
= 5 · 4096 46 = 4096
= 20,480 Multiply.
The seventh term of the sequence is 20,480.
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Chapter 7 44 Glencoe Algebra 1
7-7
Determine whether each sequence is arithmetic, geometric, or neither. Explain.
1. 7, 13, 19, 25, … 2. –96, –48, –24, –12, …
3. 108, 66, 141, 99, … 4. 3, 9, 81, 6561, …
5. 7 − 3 , 14, 84, 504, … 6. 3 −
8 , - 1−
8, - 5 −
8 , - 9 −
8 , …
Find the next three terms in each geometric sequence.
7. 2500, 500, 100, … 8. 2, 6, 18, …
9. –4, 24, –144, … 10. 4 − 5 , 2 −
5 , 1 −
5 , …
11. –3, –12, –48, … 12. 72, 12, 2, …
13. Write an equation for the nth term of the geometric sequence 3, – 24, 192, …. Find the ninth term of this sequence.
14. Write an equation for the nth term of the geometric sequence 9 − 16
, 3 − 8 , 1 −
4 , ….
Find the seventh term of this sequence.
15. Write an equation for the nth term of the geometric sequence 1000, 200, 40, …. Find the fifth term of this sequence.
16. Write an equation for the nth term of the geometric sequence – 8, – 2, - 1 − 2 , ….
Find the eighth term of this sequence.
17. Write an equation for the nth term of the geometric sequence 32, 48, 72, …. Find the sixth term of this sequence.
18. Write an equation for the nth term of the geometric sequence 3 − 100
, 3 − 10
, 3, …. Find the ninth term of this sequence.
Skills PracticeGeometric Sequences as Exponential Functions
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Chapter 7 45 Glencoe Algebra 1
7-7
Determine whether each sequence is arithmetic, geometric, or neither. Explain.
1. 1, -5, -11, -17, … 2. 3, 3 − 2 , 1, 3 −
4 , …
3. 108, 36, 12, 4, … 4. -2, 4, -6, 8, …
Find the next three terms in each geometric sequence.
5. 64, 16, 4, … 6. 2, -12, 72, …
7. 3750, 750, 150, … 8. 4, 28, 196, …
9. Write an equation for the nth term of the geometric sequence 896, -448, 224, … . Find the eighth term of this sequence.
10. Write an equation for the nth term of the geometric sequence 3584, 896, 224, … . Find the sixth term of this sequence.
11. Find the sixth term of a geometric sequence for which a2 = 288 and r = 1 − 4
.
12. Find the eighth term of a geometric sequence for which a3 = 35 and r = 7.
13. PENNIES Thomas is saving pennies in a jar. The first day he saves 3 pennies, the second day 12 pennies, the third day 48 pennies, and so on. How many pennies does Thomas save on the eighth day?
PracticeGeometric Sequences as Exponential Functions
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Chapter 7 46 Glencoe Algebra 1
7-7
1. WORLD POPULATION The CIA estimates the world population is growing at a rate of 1.167% each year. The world population for 2007 was about 6.6 billion.
a. Write an equation for the world population after n years. (Hint: The common ratio is not 0.01167.)
b. What will the estimated world population be in 2017?
2. MUSEUMS The table shows the annual visitors to a museum in millions. Write an equation for the projected number of visitors after n years.
3. BANKING Arnold has a bank account with a beginning balance of $5000. He spends one-fifth of the balance each month. How much money will be in the account after 6 months?
4. POPULATION The table shows the projected population of the United States through 2050. Does this table show an arithmetic sequence, a geometric sequenceor neither? Explain.
Source: U.S. Census Bureau
5. SAVINGS ACCOUNTS A bank offers a savings account with a 0.5% return each month.
a. Write an equation for the balance of a savings account after n months. (Hint: The common ratio is not 0.005.)
b. Given an initial deposit of $500, what will the account balance be after 15 months?
Word Problem PracticeGeometric Sequences as Exponential Functions
YearVisitors
(millions)
1 4
2 6
3 9
4 13 1 − 2
n ?
YearProjected
Population
2000 282,125,000
2010 308,936,000
2020 335,805,000
2030 363,584,000
2040 391,946,000
2050 419,854,000
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Chapter 7 47 Glencoe Algebra 1
7-7
Pay it ForwardThe idea behind “pay it forward” is that on the first day, one person does a good deed for three different people. Then, on the second day, those three people will each perform good deeds for 3 more people, so that on Day 2, there are 3 × 3 or 9 good deeds being done. Continue this process to fill in the chart. A tree diagram will help you fill in the chart.
1. Graph the data you found in the chart as ordered pairs and connect with a smooth curve.
2. What type of function is your graph from Exercise 1? Write an equation that can be used to determine the number of good deeds on any given day, x.
3. How many good deeds will be performed on Day 21?
The formula T = 3 n + 1 - 3 − 2 can be used to determine the total number of good deeds that
have been performed, where n represents the day. For example, on Day 2, there have been 3 + 9 or 12 good deeds performed. Using the formula, you get, 3 2 + 1 - 3 −
2 or 3 3 - 3 −
2 + 27 - 3 −
2 or
a total of 12 good deeds performed.
4. Use the formula to determine the approximate number of good deeds that have been performed through Day 21.
5. Look up the world population. How does your number from Exercise 4 compare to the world population?
Person 1
Day 2Day 1
New Person 2
New Person 1
New Person 3
y
xO
240210180
120150
906030
432 7 8651
Day# of
Deeds
0 1
1 3
2 9
3
4
5
Enrichment
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Chapter 7 48 Glencoe Algebra 1
Study Guide and Intervention Recursive Formulas
7-8
Using Recursive Formulas A recursive formula allows you to find the nth term of a sequence by performing operations on one or more of the terms that precede it.
Find the first five terms of the sequence in which a 1 = 5 and a n = -2 a n - 1 + 14, if n ≥ 2.
The given first term is a 1 = 5. Use this term and the recursive formula to find the next four terms. a 2 = -2 a 2 - 1 + 14 n = 2 a 4 = -2 a 4 - 1 + 14 n = 4
= -2 a 1 + 14 Simplify. = -2 a 3 + 14 Simplify.
= -2(5) + 14 or 4 a 1 = 5 = -2(6) + 14 or 2 a 3 = 6
a 3 = -2 a 3 - 1 + 14 n = 3 a 5 = -2 a 5 - 1 + 14 n = 5
= -2 a 2 + 14 Simplify. = -2 a 4 + 14 Simplify.
= -2(4) + 14 or 6 a 2 = 4 = -2(2) + 14 or 10 a 4 = 2
The first five terms are 5, 4, 6, 2, and 10.
ExercisesFind the first five terms of each sequence.
1. a 1 = -4, a n = 3 a n - 1 , n ≥ 2 2. a 1 = 5, a n = 2a n - 1 , n ≥ 2
3. a 1 = 8, a n = a n - 1 - 6, n ≥ 2 4. a 1 = -32, a n = a n - 1 + 13, n ≥ 2
5. a 1 = 6, a n = -3 a n - 1 + 20, n ≥ 2 6. a 1 = -9, a n = 2 a n - 1 + 11, n ≥ 2
7. a 1 = 12, a n = 2 a n - 1 - 10, n ≥ 2 8. a 1 = -1, a n = 4 a n - 1 + 3, n ≥ 2
9. a 1 = 64, a n = 0.5 a n - 1 + 8, n ≥ 2 10. a 1 = 8, a n = 1.5 a n - 1 , n ≥ 2
11. a 1 = 400, a n = 1 − 2 a n - 1 , n ≥ 2 12. a 1 = 1 −
4 , a n = a n - 1 + 3 −
4 , n ≥ 2
Example
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Chapter 7 49 Glencoe Algebra 1
Study Guide and Intervention (continued)
Recursive Formulas
Writing Recursive Formulas Complete the following steps to write a recursive formula for an arithmetic or geometric sequence.
Step 1 Determine if the sequence is arithmetic or geometric by fi nding a common
difference or a common ratio.
Step 2 Write a recursive formula.
Arithmetic Sequences a n = a n - 1 + d, where d is the common difference
Geometric Sequences an = r · an - 1, where r is the common ratio
Step 3 State the fi rst term and the domain for n.
Write a recursive formula for 216, 36, 6, 1, … .
Step 1 First subtract each term from the term that follows it.216 - 36 = 180 36 − 6 = 30 6 - 1 = 5There is no common difference. Check for a common ratio by dividing each term by the term that precedes it.
36 − 216
= 1 − 6 6 −
36 = 1 −
6 1 −
6 = 1 −
6
There is a common ratio of 1 − 6 . The sequence is geometric.
Step 2 Use the formula for a geometric sequence. a n = r · a n - 1 Recursive formula for geometric sequence
a n = 1 − 6 a n - 1 r = 1 −
6
Step 3 The first term a 1 is 216 and n ≥ 2.
A recursive formula for the sequence is a 1 = 216, a n = 1 − 6 a n - 1 , n ≥ 2.
ExercisesWrite a recursive formula for each sequence.
1. 22, 16, 10, 4, … 2. -8, -3, 2, 7, …
3. 5, 15, 45, 135, … 4. 243, 81, 27, 9, …
5. −3, 14, 31, 48, … 6. 8, -20, 50, -125, …
7-8
Example
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Chapter 7 50 Glencoe Algebra 1
Skills PracticeRecursive Formulas
7-8
Find the first five terms of each sequence.
1. a 1 = -11, a n = a n − 1 − 7, n ≥ 2 2. a 1 = 14, a n = a n − 1 + 6.5, n ≥ 2
3. a 1 = -3, a n = 3a n − 1 + 10, n ≥ 2 4. a 1 = 187.5, a n = −0.8 a n - 1 , n ≥ 2
5. a 1 = 1 − 2 , a n = 3 −
2 a n - 1 + 1 −
4 , n ≥ 2 6. a 1 = 1 −
5 , a n = 5 −
2 a n - 1 - 1 −
2 , n ≥ 2
Write a recursive formula for each sequence.
7. 7, 28, 112, 448, … 8. 73, 52, 31, 10, …
9. 4, 1, 1 − 4 , 1 −
16 , … 10. -37, -15, 7, 29, …
11. 0.25, 0.37, 0.49, 0.61, … 12. 64, -80, 100, -125, 156.25, …
For each recursive formula, write an explicit formula. For each explicit formula, write a recursive formula.
13. a 1 = 38, a n = a n - 1 - 17, n ≥ 2 14. a n = 5n - 16
15. a n = 50(0.75 ) n - 1 16. a 1 = 16, a n = 4 a n − 1 , n ≥ 2
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Chapter 7 51 Glencoe Algebra 1
PracticeRecursive Formulas
Find the first five terms of each sequence.
1. a 1 = 25, a n = a n - 1 - 12, n ≥ 2 2. a 1 = -101, a n = a n - 1 + 38, n ≥ 2
3. a 1 = 3.3, a n = a n - 1 + 2.7, n ≥ 2 4. a 1 = 7, a n = -3 a n - 1 + 20, n ≥ 2
5. a 1 = 20, a n = 1 − 5 a n - 1 , n ≥ 2 6. a 1 = 2 −
3 , a n = 1 −
3 a n - 1 - 2 −
9 , n ≥ 2
Write a recursive formula for each sequence.
7. 80, -40, 20, -10, … 8. 87, 52, 17, -18, …
9. 1 − 3 , 4 −
15 , 16 −
75 , 64 −
375 , … 10. 4 −
5 , 3 −
10 , - 1 −
5 , - 7 −
10 , …
11. 2.6, 5.2, 7.8, 10.4, … 12. 100, 120, 144, 172.8, …
13. PIZZA The total costs for ordering one to five cheese pizzas from Luigi’s Pizza Palace are shown.
a. Write a recursive formula for the sequence.
b. Write an explicit formula for the sequence.
7-8
Total Number of
Pizzas OrderedCost
1 $7.00
2 $12.50
3 $18.00
4 $23.50
5 $29.00
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Chapter 7 52 Glencoe Algebra 1
Word Problem PracticeRecursive Formulas
1. ASSEMBLY An assembly line can create 175 widgets in one hour, 350 widgets in two hours, 525 widgets in three hours, 700 widgets in four hours, and so on.
a. Find the next 5 terms in the sequence.
b. Write a recursive formula for the sequence.
c. Write an explicit formula for the sequence.
2. PAPER A piece of paper is folded several times. The number of sections into which the piece of paper is divided after each fold is shown below.
Number of Folds Sections
1 2
2 4
3 8
4 16
5 32
a. Find the next 5 terms in the sequence.
b. Write a recursive formula for the sequence.
c. Write an explicit formula for the sequence.
3. CLEANING An equation for the cost a n in dollars that a carpet cleaning company charges for cleaning n rooms is a n = 50 + 25(n - 1). Write a recursive formula to represent the cost a n.
4. SAVINGS A recursive formula for the balance of a savings account a n in dollars at the beginning of year n is a 1 = 500, an = 1.05 a n - 1 , n ≥ 2. Write an explicit formula to represent the balance of the savings account a n .
5. SNOW A snowman begins to melt as the temperature rises. The height of the snowman in feet after each hour is shown.
Hour Height (ft)
1 6.0
2 5.4
3 4.86
4 4.374
a. Write a recursive formula for the sequence.
b. Write an explicit formula for the sequence.
7-8
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Chapter 7 53 Glencoe Algebra 1
EnrichmentArithmetic Series
7-8
Consider a situation in which an uncle gives his niece a dollar amount equal to her age each year on her birthday. An arithmetic sequence that represents this situation is 1, 2, 3, … . How much total money will the niece have received by her 30th birthday?
When the terms of an arithmetic sequence are added, an arithmetic series is formed. The solution of the problem above is the sum of the arithmetic series 1 + 2 + 3 + … + 30.
If we write the series twice, as shown below, and add the terms in each column, we can see a pattern. 1 + 2 + 3 + 4 + ... + 27 + 28 + 29 + 30 30 + 29 + 28 + 27 + ... + 4 + 3 + 2 + 1
31 + 31 + 31 + 31 + ... + 31 + 31 + 31 + 31
The sum of each pair of terms is 31. Multiplying 31 by the number of terms in the bottom row, 30, gives us the sum of the bottom row, or 930. Since the series was written twice, and resultantly, each term in the series was accounted for twice, we can divide 930 by 2 and find that the sum of the series 1 + 2 + 3 + … + 30 is 465.
1. Write an expression to represent the sum of the series above using the first term 1, the last term 30, and the number of terms in the series 30.
2. Write an expression to represent the sum of an arithmetic series with n terms, first term a 1 , and last term a n .
Use the expression that you found in Exercise 2 to find the sum of each arithmetic series.
3. 1 + 2 + 3 + … + 100 4. 5 + 10 + 15 + … + 100
5. 1 + 3 + 5 + … + 29 6. 2 + 4 + 6 + … + 60
7. 6 + 13 + 20 + … + 125 8. 8 + 12 + 16 + … + 84
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Chapter 7 55 Glencoe Algebra 1
7 SCORE Student Recording SheetUse this recording sheet with pages 458–459 of the Student Edition.
7a.
7b.
8.
9.
10. (grid-in)
10.
Record your answers for Question 11 on the back of this paper.
Extended Response
Read each question. Then fill in the correct answer.
Multiple Choice
Record your answer in the blank.
For gridded response questions, also enter your answer in the grid by writing each number or symbol in a box. Then fill in the corresponding circle for that number or symbol.
1. A B C D
2. F G H J
3. A B C D
4. F G H J
5. A B C D
6. F G H J
Short Response/Gridded Response
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
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Chapter 7 56 Glencoe Algebra 1
7 Rubric for Scoring Extended Response
General Scoring Guidelines
• If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended-response questions require the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete response for full credit.
Exercise 11 Rubric
Score Specifi c Criteria
4 Part a identifies Mercury as the planet closest to the Sun, because it has the smallest exponent. In part b, students set up and solve the expression 2.28 × 108
− 1.50 × 108
to find that Mars is about 1.52 times further from the Sun than Earth. In part c, students set up and solve the expression 1.43 × 109
− 3 × 105
to find that it takes
approximately 4767 seconds for light from the Sun to reach Saturn.
3 A generally correct solution, but may contain minor flaws in reasoning or computation.
2 A partially correct interpretation and/or solution to the problem.
1 A correct solution with no evidence or explanation.
0 An incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given.
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Chapter 7 Quiz 2 (Lessons 7-3 and 7-4)
7
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Chapter 7 57 Glencoe Algebra 1
7 SCORE
Simplify.
1. (r3)(2r5) 2. (x5)4
3. (-4t2n3)(3tn4) 4. (-5x4y2)3
5. (2cd)2(-4c3)2 6. (5y2w4)2 + 2( yw2)4
Simplify. Assume that no denominator is equal to zero.
7. 6 15 − 6 9
8. y 8
− y 3
9. r 6 n -7 − r 4 n 2
10. MULTIPLE CHOICE Write the ratio of the area of a circle with radius r to the circumference of the same circle.
A 2 − r B 2 C r − 2 D 1 −
2r
Simplify.
1. 4 √ �� 81 2. 4
3 − 2
Solve each equation.
3. 5 x = 125 4. 2 5x - 4 = 64
5. Write 2 √ �� 7xy in exponential form.
Express each number in scientific notation.
6. 14,000,000 7. 0.0000308
8. MULTIPLE CHOICE Evaluate (4 × 107)(3.6 × 10-4).
A 1.11 × 103 C 1.44 × 102
B 1.44 × 104 D 1.44 × 10-27
Evalute each quotient. Express the results in both scientific notation and standard form.
9. 7.2 × 10 4 − 8 × 1 0 -3
10. -3.6 × 1 0 -5 − 6 × 1 0 3
Chapter 7 Quiz 1 (Lessons 7-1 and 7-2)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
SCORE
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Chapter 7 Quiz 4 (Lessons 7-7 and 7-8)
7
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Chapter 7 58 Glencoe Algebra 1
7 SCORE Chapter 7 Quiz 3(Lessons 7-5 and 7-6)
SCORE
Graph each function. Find the y-intercept and state the domain and range.
1. y = ( 1 − 3 )
x
2. y = 4(2)x - 1
Robin invests $1500 at 4.85% compounded quarterly.
3. Write an equation to represent the amount of money he will have in n years.
4. How much money will Robin have in 12 years?
5. MULTIPLE CHOICE The population of Camden, New Jersey, has been decreasing by 0.12% a year on average. If this trend continues, and the population was79,318 in 2006, estimate Camden’s population in 2015.
A 71,152 C 78,465 B 78,461 D 80,179
1.
y
xO
2.
y
xO
3.
4.
5.
1. Determine whether the sequence 32, 16, 8, 4, . . . is arithmetic, geometric, or neither. Explain.
2. Find the next three terms of the geometric sequence -3, -12, -48, ... .
3. MULTIPLE CHOICE What is the eighth term of the geometric series -2, 10, -50, ...?
A -781,250 C 156,250 B -156,250 D 781,250
Write a recursive formula for each sequence. 4. 3, 20, 37, 54, …
5. 125, -25, 5, - 1 − 5
1.
2.
3.
4.
5.
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Chapter 7 59 Glencoe Algebra 1
7 SCORE
Part I Write the letter for the correct answer in the blank at the right of each question.
1. Simplify (n5)(n2)(r3)(r4).
A n10r12 B n7r7 C nr7 D nr14
2. Simplify (3w2r)2( - 2w5r2)3.
F -72w19r8 G 72w12r7 H -36w32r10 J 36w19r6
Simplify. Assume the denominator is not equal to zero.
3. m 6 n 3 − m 2 n 6
A m 4 − n 3
B - m 4 − n 3
C - m 8 − n 3
D m 8 − n 3
4. ( z 2 w -1 ) 3 −
( z 3 w 2 ) 2
F 1 − w 7
G z 12 − w 7
H w J 1 − w
5. Solve 2 3x + 10 = 128.
A 3 B 2 C 1 D -1 6. Express 0.000702 in scientific notation.
F 7.02 × 10-3 H 7.02 × 10-4 G 7.02-4 J 7.02 × 10-5
7. Evaluate 6.08 × 10 7 − 3.8 × 10 -2
.
A 1.6 × 105 B 1.6 × 109 C 2.3104 × 106 D 2.3104 × 1010
Part II Evalute each product. Express the results in both scientific notation and standard form.
8. (4.2 × 109)(1.6 × 10-5)
9. (7.8 × 10-3)(4 × 10-4)
Simplify. Assume that no denominator is equal to zero.
10. 2 x 3 y 5 −
5( x 4 y 2 ) 3 11.
-10 m -1 y 0 r −
-14 m -7 y -3 r -4
Solve each equation.
12. 8 x = 16
13. 21 6 x + 1 = 6
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Chapter 7 Mid-Chapter Test (Lessons 7-1 through 7-4)
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Chapter 7 60 Glencoe Algebra 1
7 SCORE Chapter 7 Vocabulary Test
State whether each sentence is true or false. If false, replace the underlinedword or phrase to make a true sentence.
1. The zero exponent property tells us that any nonzero number raised to the zero power is 1.
2. A very large or very small number written in the form a × 10n, where 1 ≤ a < 10 and n is an integer, is said to be in scientific notation.
3. The scientific notation of a quantity is the number rounded to the nearest power of 10.
4. The negative exponent of a geometric sequence can be found by dividing any term by its previous term.
5. Constants are monomials that are real numbers.
6. The equation A = P (1 + r − n ) nt
is the general equation for compound interest.
7. A recursive formula allows you to find the nth term of a sequence by performing operations to one or more of the terms that precede it.
8. Exponential decay is when an initial amount decreases by the same percent over a given period of time.
9. A number, a variable, or a product of a number and one or more variables is a geometric sequence.
Define each term in your own words.
10. exponential function
11. geometric sequence
common ratio
compound interest
constant
exponential decay
exponential function
exponential growth
geometric sequence
monomial
negative exponent
nth root
order of magnitude
rational exponent
recursive formula
scientifi c notation
zero exponent
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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Chapter 7 61 Glencoe Algebra 1
7 SCORE Chapter 7 Test, Form 1
Write the letter for the correct answer in the blank at the right of each question.
1. Simplify y5 � y3.
A y2 B y8 C y15 D 2y8
2. Simplify (b4)3.
F b7 G 3b4 H b12 J 3b7
3. Simplify a7 −
a4 . Assume the denominator is not equal to zero.
A a11 B a28 C a3 D 1
4. A rectangle has a length of 25x3 and a width of 5x2. Find the area in square units.
F 25x6 G 25x5 H 125x6 J 125x5
5. Simplify m5r2 −
m2r3 . Assume the denominator is not equal to zero.
A m7r5 B m3 − r C m3r D r −
m3
6. Express 0.000024 in scientific notation.
F 2.4 × 105 G 0.24 × 10-4 H 2.4 × 10-4 J 2.4 × 10-5
7. Evaluate (7 × 108)(2.4 × 10-4).
A 1.68 × 104 B 2.92 × 104 C 1.68 × 105 D 1.68 × 1013
8. Evaluate 16 3 − 4 .
F 2 G 4 H 8 J 32
9. Solve 3 x + 2 = 81.
A 0 B 1 C 2 D 3
10. Which equation corresponds to the graph shown? F y = 2x + 2 H y = 2x - 2
G y = ( 1 − 2 )
x
- 2 J y = ( 1 − 2 )
x
+ 2
11. What is the y-intercept on the graph shown?
A 1 − 2 B 1 C 0 D -1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
y
xO
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Chapter 7 62 Glencoe Algebra 1
7 Chapter 7 Test, Form 1 (continued)
12. TOURNAMENTS A chess tournament starts with 16 people competing.
The exponential function y = 16 ( 1 − 2 )
x
describes how many people are
remaining in the tournament after x rounds. How many people are left in the tournament after 2 rounds?
F 4 G 2 H 8 J 1
13. INVESTMENTS Determine the amount of an investment if $1000 is invested at an interest rate of 8% compounded quarterly for 2 years.
A $1160.00 B $1171.66 C $1040.40 D $1166.40
14. BIOLOGY If y = 10(2.5) t represents the number of bacteria in a culture at time t, how many will there be at time t = 6?
F 2441 G 244 H 24 J none
15. DEPRECIATION A $60,000 piece of machinery depreciates in value at a rate of 11% per year. About what will its value be in 5 years?
A $47,526 B $42,298 C $33,504 D $37,645
16. Which is the equation for the nth term of the geometric sequence -2, 8, -32, . . . ?
F a n = -2 � 4 n H a n = - 2 · 4 n-1 G a n = 4 � (-2 ) n J a n = - 2 · (-4)n-1
17. What is the ninth term of the geometric sequence 3, 9, 27, . . .? A 2187 B 6561 C 19,683 D 59,049
18. Find the third term of the sequence in which a 1 = 12 and a n = 5 a n - 1 - 14, if n ≥ 2.
F 1 G 46 H 216 J 1066
19. Find an explicit formula for a 1 = 17, a n = a n - 1 + 4, n ≥ 2. A a n = 4n + 13 C a n = 4n + 17 B a n = n + 4 D a n = 17n + 4
20. Find a recursive formula for the arithmetic sequence 18, 12, 6, 2, ... .
F a 1 = 18, a n = -6 a n - 1 , n ≥ 2 H a 1 = 18, a n = 2 − 3 a n - 1 , n ≥ 2
G a 1 = 18, a n = a n - 1 - 6, n ≥ 2 J a 1 = 18, a n = 1 − 2 a n - 1 + 9, n ≥ 2
Bonus Simplify (3n+1)(32n)4.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
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Chapter 7 63 Glencoe Algebra 1
7 SCORE
Write the letter for the correct answer in the blank at the right of each question.
1. Simplify (x3)8.
A x24 B x11 C 8x24 D 8x11
2. Simplify (-2hk)4(4h3k5)2.
F 2h24k40 G -64h9k11 H - 256h10k14 J 256h10k14
3. Simplify 36 b 4 c 2 − 9 b -1 c 5
. Assume the denominator is not equal to zero.
A 27 b 4 − c 3
B 4 b 4 − c 3
C 27 b 3 − c 3
D 4 b 5 − c 3
4. Simplify (3 y 4 n 6 ) 2
− ( y 2 n -3 ) 4
. Assume the denominator is not equal to zero.
F 9 − y 16
G 9 − n 24
H 9y16 J 9n24
5. Which monomial represents the number of square units in the area of a circle with radius 4x3 units?
A 16πx6 B 8πx6 C 16πx9 D 8πx5
6. Express 46,100,000 in scientific notation.
F 4.61 × 107 G 4.61 × 106 H 4.61 × 105 J 4.61 × 108
7. Evaluate 7 × 1 0 4 − 1.4 × 1 0 -5
.
A 5 × 109 B 5 × 10-20 C 5 × 10-1 D 5 × 101
8. ATTENDANCE The total attendance for a professional baseball team this season was 3.24 × 1 0 6 and two years ago was 2.43 × 1 0 6 . About how many times as large was this season’s attendance as attendance two years ago?
F 0.8 G 0.9 H 1.1 J 1.3
9. Write 10 y 1 −
2 in radical form.
A √ �� 10y B 10 √ � y C 10 √ �� 10y D y √ �� 10
10. Evaluate 8 1 3 − 4 .
F 3 G 9 H 27 J 243
11. Solve 5 x - 2 = 125.
A 2 B 3 C 4 D 5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Chapter 7 Test, Form 2A
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Chapter 7 64 Glencoe Algebra 1
7
12. Which is the equation for the nth term of the geometric sequence -4, 8, -16, ... ?
F a n = - 4 · 2 n-1 H a n = -4 . (-2) n-1 G a n = -2 . (-4) n-1 J a n = - 2 · 4 n
13. Which equation represents exponential growth? A y = 5( 0.84) x B y = 5x C y = 0.3x3 D y = 5 (1.06) x
14. Which equation corresponds to the graph shown? F y = ( 3) x + 1 H y = 2( 3 x ) G y = 2( 3 x + 1) J y = (2 . 3) x + 1
15. A weightlifter can increase the weight W(x) that she can lift according to W(x) = 315(1.0 5) x , where x represents the number of training cycles completed. How much will she lift after 4 training cycles?
A 365 lb B 383 lb C 378 lb D 402 lb
16. BIOLOGY A certain fast-growing bacteria increases 6% per minute. If there are 100 bacteria now, about how many will there be 12 minutes later?
F 172 G 201 H 48 J 190
17. POPULATION A city’s population is about 954,000 and is decreasing at an annual rate of 0.1%. Predict the population in 50 years.
A 577,176 B 906,300 C 1,002,888 D 907,450
18. Find the third term of the sequence in which a 1 = 7 and a n = -2 a n - 1 + 11, if n ≥ 2.
F -23 G -3 H 5 J 17
19. Find an explicit formula for a 1 = -4, a n = a n - 1 + 9, n ≥ 2. A a n = 9n - 13 C a n = 9n - 4 B a n = n + 9 D a n = -4n + 9
20. Find a recursive formula for the arithmetic sequence 24, 32, 40, 48, ... . F a 1 = 24, a n = 8 a n - 1 , n ≥ 2 H a 1 = 24, a n = 4 −
3 a n - 1 , n ≥ 2
G a 1 = 24, a n = 1 − 2 a n - 1 + 20, n ≥ 2 J a 1 = 24, a n = a n - 1 + 8, n ≥ 2
Bonus Simplify 7 x - 3 − 7 3x - 1
.
Chapter 7 Test, Form 2A (continued)
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
y
xO
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Chapter 7 65 Glencoe Algebra 1
7 SCORE
Write the letter for the correct answer in the blank at the right of each question.
1. Simplify (m4)2.
A 6m B m8 C m6 D 2m4
2. Simplify (-2xy2)4(2x3y4)2.
F 4x24y32 G -8x9y6 H 64x10y16 J -4x10y16
3. Simplify 6 n -3 y
− 2 n -1 y -3
. Assume the denominator is not equal to zero.
A 4 y 3
− n 2
B 3 y 4
− n 2
C 3 − n 4 y 2
D 3n2 −
y4
4. Simplify ( a -2 b 4 ) -6 −
( a 4 b -8 ) 3 . Assume the denominator is not equal to zero.
F ab3 G 1 H a 24 − b 48
J b 48 − a 24
5. Which monomial represents the number of square units in the area of a circle with radius 3x3 units?
A 9πx6 B 6πx6 C. 9πx9 D 6πx5
6. Express 8,450,000 in scientific notation.
F 8.45 × 104 G 8.45 × 107 H 8.45 × 105 J 8.45 × 106
7. Evaluate 4.65 × 1 0 -4 − 5 × 1 0 -6
.
A 9.3 × 1011 B 9.3 × 101 C 9.3 × 102 D 9.3 × 100
8. SOLAR SYSTEM The average distance Earth is from the Sun is about 9.296 × 1 0 7 miles, and the average distance Mars is from the Sun is about 1.4162 × 1 0 8 . About how many times as far is Mars from the Sun as Earth is from the Sun?
F 0.7 G 0.9 H 1.3 J 1.5
9. Write (8x ) 1 − 2 in radical form.
A 8 √ � x B √ � 8x C 8 √ � 8x D x √ � 8
10. Evaluate 12 5 2 − 3 .
F 5 G 25 H 625 J 3125
11. Solve 6 x + 1 = 1296.
A 1 B 2 C 3 D 4
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Chapter 7 Test, Form 2B
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Chapter 7 66 Glencoe Algebra 1
7
12. Which is the equation for the nth term of the geometric sequence 6, 12, 24, ... ? F a n = 6 . 2 n G a n = 2 . 3 n H a n = 3 . 2 n J a n = 3 . 2 n-1
13. Which equation represents exponential decay? A y = 0.5x3 B y = 0.5x2 - x C y = 0.5(1 .07) x D y = 0.5(.8 7) x
14. Which equation corresponds to the graph shown? F y = 3 x + 2 H y = 2( 3 x ) G y = 2( 3 x + 1) J y = (2 . 3 ) x + 1
15. A weight lifter can deadlift 275 pounds. She can increase the weight W(x) that she can lift according to the function W(x) = 275(1.05)x, where x represents the number of training cycles completed. How much will she deadlift after 5 training cycles?
A 334 lb B 369 lb C 344 lb D 351 lb
16. POPULATION A city’s population is about 763,000 and is increasing at an annual rate of 1.5%. Predict the population of the city in 50 years.
F 1,335,250 G 826,830,628 H 358,374 J 1,606,300
17. BUSINESS A printing press valued at $120,000 depreciates 12% per year. What will be the approximate value of the printing press in 7 years?
A $19,200 B $265,282 C $49,041 D $55,728
18. Find the third term of the sequence in which a 1 = -1 and a n = 5 a n - 1 - 3, if n ≥ 2.
F -218 G -43 H -8 J 12
19. Find an explicit formula for a 1 = 10, a n = a n - 1 - 3, n ≥ 2. A a n = n - 3 C a n = -3n + 10 B a n = 10n - 3 D a n = -3n + 13
20. Find a recursive formula for the arithmetic sequence 8, -2, -12, -22, ... . F a 1 = 8, a n = -10 a n - 1 , n ≥ 2 H a 1 = 8, a n = - 1 −
2 a n - 1 + 2, n ≥ 2
G a 1 = 8, a n = a n - 1 - 10, n ≥ 2 J a 1 = 8, a n = 1 − 2 a n - 1 - 6, n ≥ 2
Bonus Simplify 32n - 1 · ( 3 5n ) .
Chapter 7 Test, Form 2B (continued)
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
y
xO
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Chapter 7 67 Glencoe Algebra 1
7 SCORE
Simplify.
1. (9t3n5)(-2tn2)
2. (w5y4)3
3. 4a3n6 + 4(a3n)6 + 4(an2)3
Simplify. Assume that no denominator is equal to zero.
4. 16 r 3 t -5 − 4 r -1 t 2
5. (-8 x 2 y 2 ) 2
− (4 x 3 y ) 3
6. Express 0.000000607 in scientific notation.
Evalute each product or quotient. Express the results inboth scientific notation and standard form.
7. (2.8 × 10-4)(7.7 × 109)
8. 8.1 × 1 0 4 − 1.8 × 1 0 -4
9. ATTENDANCE The total home attendance for a professional basketball team in 2010 was about 8.2 × 1 0 5 , and in 2008 was about 7.175 × 1 0 5 . About how many times as large was the attendance in 2010 as the attendance in 2008?
Solve each equation.
10. 3 6 x - 2 = 6
11. 4 3x - 2 = 256
12. 3 2 x + 3 = 2
Chapter 7 Test, Form 2C
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
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Chapter 7 68 Glencoe Algebra 1
7
Simplify.
13. 6 4 5 − 6
14. 8 1 5 − 4
Write each expression in radical form.
15. 2 2 1 − 3
16. 3 x 1 − 4
17. A weight lifter can bench-press 165 pounds. She plans to increase the weight W(x) in pounds that she is lifting according to the function W(x) = 165(1.05)x, where x represents the number of training cycles she completes. How much will she bench-press after 4 training cycles?
18. Graph y = 7x. Find the y-intercept and state the domain and range.
19. INVESTMENTS Determine the amount of an investment if $700 is invested at an interest rate of 8% compounded monthly for 9 years.
20. BUSINESS A new welding machine valued at $38,000 depreciates at a steady rate of 9% per year. What is the value of the welding machine in 10 years?
21. Write an equation for the nth term of the geometric sequence -3, 9, -27,. . . .
Find the first three terms of each sequence.
22. a 1 = 5, a n = a n - 1 - 3, n ≥ 2
23. a 1 = 3, a n = 2 a n - 1 + 4, n ≥ 2
Write a recursive formula for each sequence.
24. 18, 29, 40, 51, …
25. 2, −12, 72, −432, …
Bonus Find the first term of the geometric sequence with a 6 = 256 and a 7 = 1024.
Chapter 7 Test, Form 2C (continued)
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
y
xO
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Chapter 7 69 Glencoe Algebra 1
7 SCORE
Simplify.
1. (3a2b5)(-2ab3)
2. (w3z7)3
3. 4a4b8 + 2(ab2)4 + 4(a2b4)2
Simplify. Assume that no denominator is equal to zero.
4. 4 a -3 d 2 − 8 a 2 d -5
5. (3 r 3 t 5 ) 3 −
(-3 r 2 t 7 ) 2
6. Express 0.00000402 in scientific notation.
Evaluate each product or quotient. Express the results in both scientific notation and standard form.
7. (4.6 × 103)(9.12 × 10-7)
8. 1.6 × 1 0 -3 − 8 × 1 0 -7
9. ATTENDANCE The total home attendance for a professional football team in 2010 was about 5.44 × 1 0 5 , and in 2008 was about 4.32 × 1 0 5 . About how many times as large was the attendance in 2010 as the attendance in 2008?
Solve each equation.
10. 12 5 x - 1 = 5
11. 3 3x + 1 = 81
12. 6 4 2x + 3 = 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Chapter 7 Test, Form 2D
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Chapter 7 70 Glencoe Algebra 1
7
Simplify.
13. 100 0 2 − 3
14. 4 5 − 2
Write each expression in radical form.
15. 5 7 1 − 4
16. 10 x 1 − 3
17. A weight lifter can bench-press 145 pounds. She plans to increase the weight W(x) in pounds that she is lifting according to the function W(x) = 145(1.05)x, where x represents the number of training cycles she completes. How much will she bench-press after 5 training cycles?
18. Graph y = ( 1 − 6 )
x
. Find the y-intercept and state the
domain and range.
19. ART An oil painting originally cost $2500 and increases in value at a rate of 6% per year. Find the value of the painting after 12 years.
20. CARS A new car valued at $16,500 depreciates at a steady rate of 12% per year. What is the value of the car in 10 years?
21. Write an equation for the nth term of the geometric sequence 4, 8, 16,… .
Find the first three terms of each sequence.
22. a 1 = -4, a n = a n − 1 + 7, n ≥ 2
23. a 1 = 1, a n = 4 a n - 1 − 2, n ≥ 2
Write a recursive formula for each sequence.
24. 27, 19, 11, 3, …
25. 1296, 216, 36, 6, …
Bonus Find the first term of the geometric sequence with a 5 = 625 and a 6 = 3125.
Chapter 7 Test, Form 2D (continued)
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
y
xO
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Chapter 7 71 Glencoe Algebra 1
7 SCORE
Simplify.
1. ( 2 − 3 h 3 )
4
2. (43x+7)(42x-9)
Simplify. Assume that no denominator is equal to zero.
3. (-2m x -3 ) -4 −
8 m -5 x 0
4. ( -3 a 2 b -3 − 6 a 3 b -4
) 2
( -5b − 4 a -3
) -3
5. Express 473 in scientific notation.
Evaluate each product or quotient. Express the results in both scientific notation and standard form.
6. (5.2 × 104)(5.9 × 106)
7. 2.485 × 1 0 3 − 7.1 × 1 0 9
8. ATTENDANCE The total home attendance for a professional football team was about 5.2 × 1 0 5 . In the same year, the total home attendance for a professional baseball team was about 2.673 × 1 0 6 . About how many times as large was the attendance for the baseball team as the attendance for the football team?
Solve each equation.
9. 4 3x - 2 = 256
10. 62 5 x - 1 = 5
11. 3 3x + 2 = 729
12. 25 6 4x - 5 = 2
Chapter 7 Test, Form 3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
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Chapter 7 72 Glencoe Algebra 1
7
Simplify.
13. 129 6 3 − 4
14. 8 7 − 3
Write each expression in radical form.
15. 32 x 1 − 6
16. (4yz ) 1 − 8
17. WEIGHT LIFTING A weight lifter can squat 475 pounds. She plans to increase the weight W(x) in pounds that she is lifting according to the function W(x) = 475(1.05)x, where x represents the number of training cycles she completes. How much will she squat after 4 training sessions?
18. Graph y = 4(2x - 1). State the y-intercept.
19. INVESTMENTS Determine the amount of an investment if $96,000 is invested at an interest rate of 5.2% compounded daily for 3 years.
20. Suppose a car that sells for $40,000 depreciates 10% per year. How many years would it take for the car to have a value less than $25,000?
21. Write an equation for the nth term of the geometric sequence -7, 1.75, -0.4375,… .
Find the first three terms of each sequence.
22. a 1 = 2.25, a n = a n − 1 + 0.5, n ≥ 2
23. a 1 = 3.5, a n = −0.5 a n - 1 + 0.75, n ≥ 2
Write a recursive formula for each sequence.
24. 50, 3, −44, −91 …
25. 1 − 8 , 1 −
4 , 1 −
2 , 1, …
Bonus Find the first term of the geometric sequence with a 6 = 1 −
4 and a 7 = 1 −
8 .
Chapter 7 Test, Form 3 (continued)
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
y
xO
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Chapter 7 73 Glencoe Algebra 1
7
Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.
1. a. Simplify ( 4 a 3 − 2 a -2
) 4
by using the Quotient of Powers property first.
Then use the Power of a Power property.
b. Simplify ( 4 a 3 − 2 a -2
) 4
by using the Power of a Quotient property first.
Then use the Quotient of Powers property.
c. Write a statement that generalizes the results of part a and part b.
2. Give a counterexample for each statement.
a. As n increases in a geometric sequence, the value of a n will move farther away from zero.
b. In a recursive sequence, if a 1 = a 2, then a 2 = a 3 , and so on.
3. Honovi purchased a new car for $25,000 and has $5000 left to invest.
a. Choose an interest rate between 4% and 7% for Honovi’s investment, and find the length of time it would take for the investment to double.
b. Choose an annual depreciation rate from 8% to 10% for the new car that Honovi purchased, and find the length of time it would take for the car’s value to be equal to one-half of the purchase price.
c. Using the rates from part a and part b, find the length of time it would take for the investment to be equal to the value of the car. What is the value at that time?
4. The mass of Jupiter is 1.8987 × 10 27 kilograms and is roughly 317.8 times the mass of Earth. The mass of the solar system is about 1.992 × 10 30 kilograms. The Sun accounts for about 99.8% of this mass.
a. Find the mass of Earth in kilograms.
b. What is the approximate mass of all of the other objects in the solar system, not counting the Sun?
c. What percentage of the mass obtained in part b is represented by Jupiter?
Chapter 7 Extended-Response Test
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Chapter 7 74 Glencoe Algebra 1
7 SCORE Standardized Test Practice(Chapters 1–7)
1. Write y - 11 = 1 − 2 (x - 12) in standard form. (Lesson 4-2)
A y = 1 − 2 x + 5 B y = 1 −
2 x - 17 C x - 2y = -10 D x - 2y = 17
2. Ashanti wants to collect more than 50 food items for the local homeless shelter. If he has already collected 13, how many more items must he collect? (Lesson 5-1)
F 37 G at least 38 H at least 37 J more than 36
3. Solve -5n + 22 ≥ -73. (Lesson 5-3)
A {n ⎥ n ≤ 19} B {n ⎥ n ≥ 19} C {n | n ≤ - 51 − 5 } D {n ⎥ n ≥ 90}
4. Solve ⎥ 5k + 2 ⎥ > 1. (Lesson 5-5)
F {k | k < - 3 − 5 or k > - 1 −
5 } H {k | k - 3 −
5 < k < 1 −
5 }
G ∅ J {k ⎥ k is a real number.}
5. Use substitution to solve the system y = -2xof equations. (Lesson 6-2) 5x + 3y = 4
A (-4, 8) B (8, -4) C (-8, 4) D (4, -8)
6. Use elimination to solve the system x + 3y = -6of equations. (Lesson 6-3) 2x + 3y = -9
F (-2, -4) G (-6, 1) H (-3, -1) J (3, -5)
7. Simplify ( 3 2 )( 3 3 ) −
( 3 -2 )( 3 -3 ) . (Lesson 7-2)
A 310 B 312 C -1 D 1 − 3
8. Simplify 4 √ 1296 . (Lesson 7-3)
F 36 G 9 H 6 J 3
9. Evaluate (3.2 × 1 0 6 )(4.6 × 1 0 -2 ) (Lesson 7-4)
A 1.472 × 1 0 4 C 1.472 × 1 0 3
B 1.472 × 10 5 D 14.72 × 1 0 4
10. Find the sixth term of the geometric sequence -16, 40, -100, … . (Lesson 7-7)
F −15,625 H 6250
G −6250 J 1562.5
11. Simplify 24 + 6 - {23 + 7(5 - 2)}. (Lesson 1-2)
A 43 B 3 C 1 D 45
1 .
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
A B C D
A B C D
F G H J
A B C D
A B C D
F G H J
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
F G H J
F G H J
F G H J
A B C D
A B C D
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Chapter 7 75 Glencoe Algebra 1
7 Standardized Test Practice (continued)
12. Find the percent of change. (Lesson 2-7)
Original: $28 New: $21
F 25% G 7% H 33% J 14%
13. Solve a(b - c) = a − b for c. (Lesson 2-8)
A c = b 2 - 1 − b B c = -1 −
b - b C c = 1 −
b + ab D c = a −
b - ab
14. Write an equation in function notation for the relation. (Lesson 3-6)
F f(x) = -2x - 2 H f(x) = -2x + 2
G f(x) = 2x - 2 J f(x) = 1 − 2 x - 2
15. Find the slope of the line that passes through the points (-4, 4) and (6, -8). (Lesson 3-3)
A 6 − 5 B - 6 −
5 C - 5 −
6 D 5 −
6
16. Write y + 1 = 4(x - 2) in slope-intercept form. (Lesson 4-3)
F y = 4x - 3 G y = 4x + 7 H y = 4x - 9 J y = x - 9
17. Solve 14u + 9 - 10u > 21. (Lesson 5-3)
A u > 3 B u > -3 C u < 3 D u < -3
18. Simplify (4x 2) 2(-2x4) 3. (Lesson 7-1)
F -48x16 G -48x11 H 128x11 J -128x16
12.
13.
14.
15.
16.
17.
18. F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
xO
f (x)
19. Evaluate 4x(y2 - z2) if x = 3, 20. After receiving his allowance, y = 5 and z = 4. (Lesson 1-2) Spencer spent half of it on a
Mother’s Day card. He bought 2 toy cars for $0.49 each to give to his brothers, and a pack of gum for $0.35. How much did Spencer receive for his allowance if $0.42 is left over? (Lesson 2-3)
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Part 2: Gridded Response
Instructions: Enter your answer by writing each digit of the answer in a column box and
then shading in the appropriate oval that corresponds to that entry.
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pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
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nie
s, In
c.
NAME DATE PERIOD
PDF Pass
Chapter 7 76 Glencoe Algebra 1
7 Standardized Test Practice (continued)
21. Translate the sentence into an equation. The quotient of 35 and 6 plus a number is equal to twice the sum of that number and 3. (Lesson 2-1)
22. TUITION The average cost of tuition and fees at Trenton College was $33,560 for a recent school year. Two school years before, the average cost was $31,110. Find the rate of change between the two school years. (Lesson 3-3)
23. Solve 3y - 4 ≤ 7. (Lesson 5-3)
24. RECREATION Barrington needs to buy snorkels and fins for his family for their annual beach vacation. Snorkels cost $8 a set and fins cost $12 a pair. Write an inequality that represents this situation if Barrington has $62 to spend. (Lesson 5-6)
25. Graph the system of equations and determine the number of solutions it has. If it has one solution, name it. (Lesson 6-1)
x + y = 4y = x
26. Determine the best method to solve the system of equations. Then solve the system. (Lesson 6-5)
5x - 2y = 72x + 5y = -3
27. Simplify 51x-1y3
− 17x2y
Assume the denominator is not equal
to zero. (Lesson 7-2)
28. Solve 9 4n - 3 = 3 6 . (Lesson 7-3)
29. Write a recursive formula for 39, 32, 25, 18, … . (Lesson 7-8)
30. As of the end of the 2010 football season, the Dallas Cowboys and the Denver Broncos had won a total of 7 Super Bowls. The Cowboys had won 2.5 times as many Super Bowls as the Broncos. (Lesson 6-2)
a. Define variables and write a system of linear equations to find each team’s wins.
b. How many Super Bowls had the Dallas Cowboys won?
Part 3: Short Response
Instructions: Write your answers in the space provided.
21.
22.
23.
24.
25. y
xO
26.
27.
28.
29.
30a.
30b.
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An
swer
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pyr
ight
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oe/
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-Hill
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Chapter 7 A1 Glencoe Algebra 1
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
3 G
lenc
oe A
lgeb
ra 1
Ant
icip
atio
n G
uide
Exp
on
en
ts a
nd
Exp
on
en
tial
Fu
ncti
on
s
B
efor
e yo
u b
egin
Ch
ap
ter
7
•
Rea
d ea
ch s
tate
men
t.
•
Dec
ide
wh
eth
er y
ou A
gree
(A
) or
Dis
agre
e (D
) w
ith
th
e st
atem
ent.
•
Wri
te A
or
D i
n t
he
firs
t co
lum
n O
R i
f yo
u a
re n
ot s
ure
wh
eth
er y
ou a
gree
or
disa
gree
, wri
te N
S (
Not
Su
re).
ST
EP
1A
, D, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
Wh
en m
ult
iply
ing
two
pow
ers
that
hav
e th
e sa
me
base
, m
ult
iply
th
e ex
pon
ents
.D
2.
( k 3 )
4 is
equ
ival
ent
to k
12 .
A 3
. T
o di
vide
tw
o po
wer
s th
at h
ave
the
sam
e ba
se, s
ubt
ract
th
e ex
pon
ents
.A
4.
( 2 −
5 ) 3 i
s th
e sa
me
as 2 −
5 3 .
D
5.
A p
olyn
omia
l m
ay c
onta
in o
ne
or m
ore
mon
omia
ls.
A 6
. T
he
degr
ee o
f th
e po
lyn
omia
l 3 x
2 y 3 -
5y 2 +
8 x 3
is 3
bec
ause
th
e gr
eate
st e
xpon
ent
is 3
.D
7.
A f
un
ctio
n c
onta
inin
g po
wer
s is
cal
led
an e
xpon
enti
al f
un
ctio
n.
D 8
. R
ecei
vin
g co
mpo
un
d in
tere
st o
n a
ban
k ac
cou
nt
is o
ne
exam
ple
of e
xpon
enti
al g
row
th.
A
Aft
er y
ou c
omp
lete
Ch
ap
ter
7
•
Rer
ead
each
sta
tem
ent
and
com
plet
e th
e la
st c
olu
mn
by
ente
rin
g an
A o
r a
D.
•
Did
an
y of
you
r op
inio
ns
abou
t th
e st
atem
ents
ch
ange
fro
m t
he
firs
t co
lum
n?
•
For
th
ose
stat
emen
ts t
hat
you
mar
k w
ith
a D
, use
a p
iece
of
pape
r to
wri
te a
n
exam
ple
of w
hy
you
dis
agre
e.
7 Step
1
Step
2
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-1
Cha
pte
r 7
5 G
lenc
oe A
lgeb
ra 1
Stud
y G
uide
and
Inte
rven
tion
Mu
ltip
licati
on
Pro
pert
ies o
f E
xp
on
en
ts
Mu
ltip
ly M
on
om
ials
A m
onom
ial
is a
num
ber,
a va
riab
le, o
r th
e pr
oduc
t of
a n
umbe
r an
d on
e or
mor
e va
riab
les
wit
h no
nneg
ativ
e in
tege
r ex
pone
nts.
An
expr
essi
on o
f th
e fo
rm x
n
is c
alle
d a
pow
er a
nd r
epre
sent
s th
e pr
oduc
t yo
u ob
tain
whe
n x
is u
sed
as a
fac
tor
n t
imes
. T
o m
ulti
ply
two
pow
ers
that
hav
e th
e sa
me
base
, add
the
exp
onen
ts.
Pro
du
ct o
f P
ow
ers
Fo
r a
ny n
um
be
r a
an
d a
ll in
teg
ers
m a
nd
n,
am ․
an
= a
m +
n.
S
imp
lify
(3x
6 )(5
x2 ).
(3x6 )
(5x2 )
= (
3)(5
)(x6
․ x2 )
Gr
oup t
he c
oeffic
ients
and t
he v
ari
able
s
=
(3
․ 5)
(x6
+ 2)
Pro
duct
of
Pow
ers
=
15x
8 S
implif
y.
Th
e pr
odu
ct i
s 15
x8 .
S
imp
lify
(-
4a3 b
)(3a
2 b5 )
.(-
4a3 b
)(3a
2 b5 )
= (
-4)
(3)(
a3 ․
a2 )(b
․ b
5 )
= -
12(a
3 +
2)(
b1 +
5)
=
-12
a5 b6
Th
e pr
odu
ct i
s -
12a5 b
6 .
Exer
cise
sS
imp
lify
eac
h e
xpre
ssio
n.
1. y
(y5 )
2.
n2
․ n
7 3.
(-7x
2 )(x
4 )
y
6 n
9 -
7x6
4. x
(x2 )
(x4 )
5.
m ․
m5
6. (-
x3 )(-
x4 )
x
7 m
6 x
7
7. (
2a2 )
(8a)
8.
(rn
)(rn
3 )(n
2 )
9. (x
2 y)(
4xy3 )
1
6a3
r2 n
6 4
x3 y
4
10. 1
−
3 ( 2a
3 b)(
6b 3 )
11
. (-
4x3 )
(-5x
7 )
12. (
-3j
2 k4 )
(2jk
6 )
4
a3 b4
20x
10
-6j
3 k10
13. (
5a 2 b
c 3 ) ( 1 −
5 a
bc 4 )
14. (
-5x
y)(4
x2 )(y
4 )
15. (
10x3 y
z2 )(-
2xy5 z
)
a
3 b2 c
7 -
20x
3 y5
-20
x4 y
6 z3
7-1
Exam
ple
1Ex
amp
le 2
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Answers (Anticipation Guide and Lesson 7-1)
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 7 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
6 G
lenc
oe A
lgeb
ra 1
Sim
plif
y Ex
pre
ssio
ns
An
exp
ress
ion
of
the
form
(xm
)n i
s ca
lled
a p
ower
of
a p
ower
an
d re
pres
ents
th
e pr
odu
ct y
ou o
btai
n w
hen
xm i
s u
sed
as a
fac
tor
n t
imes
. To
fin
d th
e po
wer
of
a po
wer
, mu
ltip
ly e
xpon
ents
.
Po
wer
of
a P
ow
erF
or
any n
um
be
r a
an
d a
ny in
teg
ers
m a
nd
p,
(am)p
= a
mp.
Po
wer
of
a P
rod
uct
Fo
r a
ny n
um
be
rs a
an
d b
an
d a
ny in
teg
er
m,
(ab
)m =
amb
m.
We
can
com
bin
e an
d u
se t
hes
e pr
oper
ties
to
sim
plif
y ex
pres
sion
s in
volv
ing
mon
omia
ls.
S
imp
lify
(-
2ab2 )
3 (a
2 )4 .
(-2a
b2 )3 (
a2 )4
= (
-2a
b2 )3 (
a8 )
Pow
er
of
a P
ow
er
=
(-
2)3 (
a3 )(b
2 )3 (
a8 )
Pow
er
of
a P
roduct
=
(-
2)3 (
a3 )(a
8 )(b
2 )3
Gro
up t
he c
oeffic
ients
and t
he v
ari
able
s
=
(-
2)3 (
a11)(
b2 )3
Pro
duct
of
Pow
ers
=
-8a
11b6
Pow
er
of
a P
ow
er
Th
e pr
odu
ct i
s -
8a11
b6 .
Exer
cise
sS
imp
lify
eac
h e
xpre
ssio
n.
1. (
y5 )2
2. (n
7 )4
3. (x
2 )5 (
x3 )
y
10
n28
x
13
4. -
3(ab
4 )3
5. (-
3ab4 )
3 6.
(4x2 b
)3
-
3a3 b
12
-27
a3 b
12
64x
6 b3
7. (
4a2 )
2 (b3 )
8.
(4x)
2 (b3 )
9.
(x2 y
4 )5
1
6a4 b
3 1
6x2 b
3 x
10y
20
10. (
2a3 b
2 )(b
3 )2
11. (
-4x
y)3 (
-2x
2 )3
12. (
-3j
2 k3 )
2 (2j
2 k)3
2
a3 b
8 5
12x
9 y3
72j
10k
9
13. (
25 a
2 b) 3 ( 1
−
5 abf
) 2 14
. (2x
y)2 (
-3x
2 )(4
y4 )
15. (
2x3 y
2 z2 )
3 (x2 z
)4
6
25a
8 b5 f
2 -
48x
4 y6
8x
17y
6 z10
16. (
-2n
6 y5 )
(-6n
3 y2 )
(ny)
3 17
. (-
3a3 n
4 )(-
3a3 n
)4 18
. -3(
2x)4 (
4x5 y
)2
1
2n12
y10
-
243a
15n
8 -
768x
14y
2
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Mu
ltip
licati
on
Pro
pert
ies o
f E
xp
on
en
ts
7-1
Exam
ple
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-1
Cha
pte
r 7
7 G
lenc
oe A
lgeb
ra 1
Skill
s Pr
acti
ceM
ult
iplicati
on
Pro
pert
ies o
f E
xp
on
en
ts
Det
erm
ine
wh
eth
er e
ach
exp
ress
ion
is
a m
onom
ial.
Wri
te y
es o
r n
o. E
xpla
in.
1. 1
1 Ye
s; 1
1 is
a r
eal n
um
ber
an
d a
n e
xam
ple
of
a co
nst
ant.
2. a
- b
No
; th
is is
th
e d
iffer
ence
, no
t th
e p
rod
uct
, of
two
var
iab
les.
3.
p 2
−
r 2 N
o;
this
is t
he
qu
oti
ent,
no
t th
e p
rod
uct
, of
two
var
iab
les.
4. y
Yes
; si
ng
le v
aria
ble
s ar
e m
on
om
ials
.
5. j
3 k Y
es;
this
is t
he
pro
du
ct o
f tw
o v
aria
ble
s.
6. 2
a +
3b
No
; th
is is
th
e su
m o
f tw
o m
on
om
ials
.
Sim
pli
fy.
7. a
2 (a3 )
(a6 )
a11
8.
x(x
2 )(x
7 ) x
10
9. (
y2 z)(
yz2 )
y3 z
3 10
. (ℓ2 k
2 )(ℓ
3 k)
�5 k
3
11. (
a2 b4 )
(a2 b
2 ) a
4 b 6
12. (
cd2 )
(c3 d
2 ) c
4 d4
13. (
2x2 )
(3x5 )
6x
7 14
. (5a
7 )(4
a2 ) 2
0a9
15. (
4xy3 )
(3x3 y
5 ) 1
2x4 y
8 16
. (7a
5 b2 )
(a2 b
3 ) 7
a7 b
5
17. (
-5m
3 )(3
m8 )
-15
m11
18
. (-
2c4 d
)(-
4cd
) 8c
5 d2
19. (
102 )
3 10
6 o
r 1,
00
0,0
00
20. (
p3 )12
p36
21. (
-6p
)2 36
p2
22. (
-3y
)3 -
27y
3
23. (
3pr2 )
2 9p
2 r4
24. (
2b3 c
4 )2
4b6 c
8
GEO
MET
RY E
xpre
ss t
he
area
of
each
fig
ure
as
a m
onom
ial.
25.
x2
x5
26
.
cd
cd
27
.
4p 9p3
x
7
c2 d
2 1
8p4
7-1
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Answers (Lesson 7-1)
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An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
8 G
lenc
oe A
lgeb
ra 1
Prac
tice
Mu
ltip
licati
on
Pro
pert
ies o
f E
xp
on
en
ts
Det
erm
ine
wh
eth
er e
ach
exp
ress
ion
is
a m
onom
ial.
Wri
te y
es o
r n
o. E
xpla
in y
our
reas
onin
g.
1.
21 a
2 −
7b
N
o;
this
invo
lves
th
e q
uo
tien
t, n
ot
the
pro
du
ct, o
f va
riab
les.
2.
b 3 c 2
−
2 Y
es;
this
is t
he
pro
du
ct o
f a
nu
mb
er,
1 −
2 , an
d t
wo
var
iab
les.
Sim
pli
fy e
ach
exp
ress
ion
.
3. (
-5x
2 y)(
3x4 )
-15
x6 y
4.
(2ab
2 f 2 )
(4a3 b
2 f 2 )
8a
4 b4 f
4
5. (
3ad
4 )(-
2a2 )
-6a
3 d4
6. (4
g3 h)(
-2g
5 ) -
8g8 h
7. (
-15
x y 4 )
(- 1 −
3 x y
3 ) 5x
2 y7
8. (-
xy)3 (
xz)
-x
4 y3 z
9. (
-18
m 2 n
) 2 (- 1 −
6 m
n 2 )
-54
m5 n
4 10
. (0.
2a2 b
3 )2
0.04
a4 b
6
11. (
2 −
3 p
) 2 4 −
9 p
2 12
. ( 1 −
4 a
d 3 ) 2
1 −
16 a
2 d 6
13. (
0.4k
3 )3
0.06
4k9
14. [
(42 )
2 ]2
48 or
65,5
36
GEO
MET
RY E
xpre
ss t
he
area
of
each
fig
ure
as
a m
onom
ial.
15.
6a2 b
4
3ab2
16
. 5x
3
17
.
6ab3
4a2 b
1
8a3 b
6 (
25x
6 )π
1
2a3 b
4
GEO
MET
RY E
xpre
ss t
he
volu
me
of e
ach
sol
id a
s a
mon
omia
l.
18.
3h2
3h2
3h2
19
.
m3 n
mn3
n
20.
7g2
3g
2
7h6
m4 n
5 (
63g
4 )π
21. C
OU
NTI
NG
A p
anel
of
fou
r li
ght
swit
ches
can
be
set
in 2
4 w
ays.
A p
anel
of
five
lig
ht
swit
ches
can
set
in
tw
ice
this
man
y w
ays.
In
how
man
y w
ays
can
fiv
e li
ght
swit
ches
be
set
? 25
or
32
22. H
OB
BIE
S T
awa
wan
ts t
o in
crea
se h
er r
ock
coll
ecti
on b
y a
pow
er o
f th
ree
this
yea
r an
d th
en i
ncr
ease
it
agai
n b
y a
pow
er o
f tw
o n
ext
year
. If
she
has
2 r
ocks
now
, how
man
y ro
cks
wil
l sh
e h
ave
afte
r th
e se
con
d ye
ar?
26 o
r 64
7-1
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-1
7-1
Cha
pte
r 7
9 G
lenc
oe A
lgeb
ra 1
1. G
RA
VIT
Y A
n e
gg t
hat
has
bee
n f
alli
ng
for
x se
con
ds h
as d
ropp
ed a
t an
ave
rage
sp
eed
of 1
6x f
eet
per
seco
nd.
If
the
egg
is
drop
ped
from
th
e to
p of
a b
uil
din
g, i
ts
tota
l di
stan
ce t
rave
led
is t
he
prod
uct
of
the
aver
age
rate
tim
es t
he
tim
e. W
rite
a
sim
plif
ied
expr
essi
on t
o sh
ow t
he
dist
ance
th
e eg
g h
as t
rave
led
afte
r x
seco
nds
.
2. C
IVIL
EN
GIN
EER
ING
A d
evel
oper
is
plan
nin
g a
side
wal
k fo
r a
new
de
velo
pmen
t. T
he
side
wal
k ca
n b
e in
stal
led
in r
ecta
ngu
lar
sect
ion
s th
at
hav
e a
fixe
d w
idth
of
3 fe
et a
nd
a le
ngt
h
that
can
var
y. A
ssu
min
g th
at e
ach
se
ctio
n i
s th
e sa
me
len
gth
, exp
ress
th
e ar
ea o
f a
4-se
ctio
n s
idew
alk
as a
m
onom
ial.
x
3 ft
3. P
RO
BA
BIL
ITY
If
you
fli
p a
coin
3 t
imes
in
a r
ow, t
her
e ar
e 23
outc
omes
th
at c
an
occu
r.
Ou
tco
mes
HH
HT
TT
HT
TT
HH
HT
HT
TH
HH
TT
HT
If
you
th
en f
lip
the
coin
tw
o m
ore
tim
es,
ther
e ar
e 23
× 2
2 ou
tcom
es t
hat
can
oc
cur.
How
man
y ou
tcom
es c
an o
ccu
r if
yo
u f
lip
the
coin
as
men
tion
ed a
bove
fou
r m
ore
tim
es?
Wri
te y
our
answ
er i
n t
he
form
2x .
4. S
POR
TS T
he
volu
me
of a
sph
ere
is g
iven
by
the
form
ula
V=
4 − 3 π r 3 ,
wh
ere
r is
th
e r
adiu
s of
th
e sp
her
e. F
ind
the
volu
me
of
air
in t
hre
e di
ffer
ent
bask
etba
lls.
Use
π
= 3
.14.
Rou
nd
you
r an
swer
s to
th
e n
eare
st w
hol
e n
um
ber.
Bal
lR
adiu
s (i
n.)
Volu
me
(in
3 )
Ch
ild’s
426
8W
om
en’s
4.5
382
Me
n’s
4.8
463
5. E
LEC
TRIC
ITY
An
ele
ctri
cian
use
s th
e fo
rmu
la W
= I
2 R ,
wh
ere
W i
s th
e po
wer
in
wat
ts, I
is
the
curr
ent
in a
mpe
res,
an
d R
is
the
resi
stan
ce i
n o
hm
s.
a.
Fin
d th
e po
wer
in
a h
ouse
hol
d ci
rcu
it
that
has
20
ampe
res
of c
urr
ent
and
5 oh
ms
of r
esis
tan
ce.
b
. If
th
e cu
rren
t is
red
uce
d by
on
e h
alf,
wh
at h
appe
ns
to t
he
pow
er?
Wor
d Pr
oble
m P
ract
ice
Mu
ltip
licati
on
Pro
pert
ies o
f E
xp
on
en
ts
16x
2 12x
29
200
0 w
atts
Th
e p
ow
er is
on
e-fo
urt
h t
he
pre
vio
us
amo
un
t.
001_
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Answers (Lesson 7-1)
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-Hill, a d
ivision o
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cGraw
-Hill C
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PDF Pass
Chapter 7 A4 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
10
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
An
Wan
g
An
Wan
g (1
920–
1990
) w
as a
n A
sian
-Am
eric
an w
ho
beca
me
one
of t
he
pion
eers
of
the
com
pute
r in
dust
ry i
n t
he
Un
ited
Sta
tes.
He
grew
up
in S
han
ghai
, Ch
ina,
bu
t ca
me
to t
he
Un
ited
Sta
tes
to f
urt
her
his
stu
dies
in
sci
ence
. In
194
8, h
e in
ven
ted
a m
agn
etic
pu
lse
con
trol
lin
g de
vice
th
at v
astl
y in
crea
sed
the
stor
age
capa
city
of
com
pute
rs. H
e la
ter
fou
nde
d h
is o
wn
com
pan
y, W
ang
Lab
orat
orie
s, a
nd
beca
me
a le
ader
in
th
e de
velo
pmen
t of
des
ktop
ca
lcu
lato
rs a
nd
wor
d pr
oces
sin
g sy
stem
s. I
n 1
988,
Wan
g w
as e
lect
ed t
o th
e N
atio
nal
In
ven
tors
Hal
l of
Fam
e.
Dig
ital
com
pute
rs s
tore
in
form
atio
n a
s n
um
bers
. Bec
ause
th
e el
ectr
onic
cir
cuit
s of
a
com
pute
r ca
n e
xist
in
on
ly o
ne
of t
wo
stat
es, o
pen
or
clos
ed, t
he
nu
mbe
rs t
hat
are
sto
red
can
co
nsi
st o
f on
ly t
wo
digi
ts, 0
or
1. N
um
bers
wri
tten
usi
ng
only
th
ese
two
digi
ts a
re c
alle
d b
inar
y n
um
ber
s. T
o fi
nd
the
deci
mal
val
ue
of a
bin
ary
nu
mbe
r, yo
u u
se t
he
digi
ts t
o w
rite
a
poly
nom
ial
in 2
. For
in
stan
ce, t
his
is
how
to
fin
d th
e de
cim
al v
alu
e of
th
e n
um
ber
1001
101 2.
(Th
e su
bscr
ipt
2 in
dica
tes
that
th
is i
s a
bin
ary
nu
mbe
r.)
1001
101 2
= 1
× 2
6 +
0 ×
25
+ 0
× 2
4 + 1
× 2
3 +
1 ×
22
+ 0
× 2
1 +
1 ×
20
= 1
× 6
4 +
0 ×
32
+ 0
× 1
6 +
1 ×
8 +
1 ×
4 +
0 ×
2 +
1 ×
1=
6
4
+
0
+
0
+
8
+
4
+
0
+
1=
77
Fin
d t
he
dec
imal
val
ue
of e
ach
bin
ary
nu
mb
er.
1. 1
111 2
15
2. 1
0000
2 16
3.
110
0001
1 2 19
5 4.
101
1100
1 2 18
5
Wri
te e
ach
dec
imal
nu
mb
er a
s a
bin
ary
nu
mb
er.
5. 8
10
00 2
6. 1
1 10
112
7. 2
9 11
101 2
8. 1
17 1
1101
012
9.
Th
e ch
art
at t
he
righ
t sh
ows
a se
t of
dec
imal
co
de n
um
bers
th
at i
s u
sed
wid
ely
in s
tori
ng
lett
ers
of t
he
alph
abet
in
a c
ompu
ter’
s m
emor
y.
Fin
d th
e co
de n
um
bers
for
th
e le
tter
s of
you
r n
ame.
Th
en w
rite
th
e co
de f
or y
our
nam
e u
sin
g bi
nar
y n
um
bers
. An
swer
s w
ill v
ary.
7-1
Th
e A
mer
ican
Sta
nd
ard
Gu
ide
for
Info
rmat
ion
Inte
rch
ang
e (A
SC
II)
A
65
N
78
a 9
7n
11
0
B
66
O
79
b
98
o
111
C
67
P
80
c 9
9p
11
2
D
68
Q
81
d
10
0q
11
3
E
69
R
82
e 101
r 11
4
F
70
S
83
f 10
2s
115
G
71
T
84
g
10
3t
116
H
72
U
85
h
10
4u
11
7
I 7
3V
8
6i
10
5v
118
J 74
W
87
j 10
6w
11
9
K
75
X
88
k 10
7x
12
0
L
76
Y
89
l 10
8y
12
1
M
77
Z
90
m
10
9z
12
2
001_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-2
Cha
pte
r 7
11
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
Div
isio
n P
rop
ert
ies o
f E
xp
on
en
ts
Div
ide
Mo
no
mia
ls T
o di
vide
tw
o po
wer
s w
ith
th
e sa
me
base
, su
btra
ct t
he
expo
nen
ts.
Qu
oti
ent
of
Po
wer
sF
or
all
inte
ge
rs m
an
d n
an
d a
ny n
on
ze
ro n
um
be
r a,
a m
−
a n =
a m
- n .
Po
wer
of
a Q
uo
tien
tF
or
any in
teg
er
m a
nd
any r
ea
l nu
mb
ers
a a
nd
b,
b ≠
0,
( a −
b ) m
= a
m
−
b m .
S
imp
lify
a 4 b
7 −
ab
2 . A
ssu
me
that
no
den
omin
ator
eq
ual
s ze
ro.
a 4 b
7 −
ab
2 = ( a
4 −
a
) ( b 7
−
b 2 ) G
roup p
ow
ers
with t
he s
am
e b
ase.
=
(a4
- 1)(
b7 -
2)
Quotient
of
Pow
ers
=
a3 b
5 S
implif
y.
Th
e qu
otie
nt
is a
3 b5 .
S
imp
lify
( 2 a
3 b 5
−
3 b 2
) 3 . Ass
um
e
that
no
den
omin
ator
eq
ual
s ze
ro.
( 2 a 3 b
5 −
3 b
2 ) 3 = (2
a 3 b
5 ) 3
−
(3 b 2 )
3 P
ow
er
of
a Q
uotient
=
2 3 ( a
3 ) 3 (
b 5 ) 3
−
(3 ) 3 (
b 2 ) 3
P
ow
er
of
a P
roduct
=
8 a 9 b
15
−
27 b 6
Pow
er
of
a P
ow
er
=
8 a 9 b
9 −
27
Quotient
of
Pow
ers
Th
e qu
otie
nt
is 8 a
9 b 9
−
27
.
Exer
cise
sS
imp
lify
eac
h e
xpre
ssio
n. A
ssu
me
that
no
den
omin
ator
eq
ual
s ze
ro.
1.
5 5 −
5 2 5
3 o
r 12
5 2.
m
6 −
m
4 m2
3.
p 5 n
4 −
p
2 n
p3 n
3
4.
a 2
−
a a
5.
x 5 y
3 −
x 5 y
2 y
6.
-
2 y 7
−
14 y 5
-
1 −
7 y 2
7.
x y 6
−
y 4 x y
2 8.
( 2 a 2 b
−
a ) 3 8
a3 b
3 9.
( 4 p 4 r
4 −
3 p
2 r 2 ) 3 64
−
27 p
6 r 6
10. ( 2 r
5 w 3
−
r 4 w 3 ) 4 1
6r 4
11. (
3 r 6 n
3 −
2 r
5 n ) 4 81
−
16 r
4 n 8
12.
r 7 n 7 t
2 −
n
3 r 3 t
2 r 4 n
4
7-2
Exam
ple
1Ex
amp
le 2
001_
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Answers (Lesson 7-1 and Lesson 7-2)
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An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
12
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Div
isio
n P
rop
ert
ies o
f E
xp
on
en
ts
Neg
ativ
e Ex
po
nen
ts A
ny
non
zero
nu
mbe
r ra
ised
to
the
zero
pow
er i
s 1;
for
exa
mpl
e,
(-0.
5)0
= 1
. An
y n
onze
ro n
um
ber
rais
ed t
o a
neg
ativ
e po
wer
is
equ
al t
o th
e re
cipr
ocal
of
the
nu
mbe
r ra
ised
to
the
oppo
site
pow
er; f
or e
xam
ple,
6 -
3 =
1 −
6 3 . T
hes
e de
fin
itio
ns
can
be
use
d to
si
mpl
ify
expr
essi
ons
that
hav
e n
egat
ive
expo
nen
ts.
Zer
o E
xpo
nen
tF
or
any n
on
ze
ro n
um
be
r a,
a0 =
1.
Neg
ativ
e E
xpo
nen
t P
rop
erty
Fo
r a
ny n
on
ze
ro n
um
be
r a
an
d a
ny in
teg
er
n, a
-n
=
1
−
a n a
nd
1
−
a -
n = a
n .
Th
e si
mpl
ifie
d fo
rm o
f an
exp
ress
ion
con
tain
ing
neg
ativ
e ex
pon
ents
mu
st c
onta
in o
nly
po
siti
ve e
xpon
ents
.
S
imp
lify
4 a
-3 b
6 −
16 a
2 b 6 c
-5 .
Ass
um
e th
at n
o d
enom
inat
or e
qu
als
zero
.
4 a
-3 b
6 −
16
a 2 b
6 c -
5 =
( 4 −
16
) ( a -
3 −
a
2 ) ( b 6 −
b 6 ) (
1 −
c -5 )
Gro
up p
ow
ers
with t
he s
am
e b
ase.
=
1 −
4 (
a -
3-2 )
( b 6-
6 )( c
5 )
Quotient
of
Pow
ers
and N
egative
Exponent
Pro
pert
ies
=
1 −
4 a
-5 b
0 c 5
Sim
plif
y.
=
1 −
4 ( 1
−
a 5 ) (1
) c 5
Negative
Exponent
and Z
ero
Exponent
Pro
pert
ies
=
c 5 −
4 a
5 S
implif
y.
Th
e so
luti
on i
s c 5 −
4 a
5 .
Exer
cise
sS
imp
lify
eac
h e
xpre
ssio
n. A
ssu
me
that
no
den
omin
ator
eq
ual
s ze
ro.
1.
2 2 −
2 -
3 25
or
32
2.
m
−
m -
4 m5
3.
p -
8 −
p
3 1 −
p 11
4.
b -4
−
b -5 b
5.
(-
x -1 y
) 0 −
4 w
-1 y
2 w
−
4 y 2
6.
( a 2 b
3 ) 2
−
(a b)
-2
a6 b
8
7.
x 4 y 0
−
x -2
x6
8.
(6 a
-1 b
) 2 −
( b
2 ) 4
36
−
a 2 b
6 9.
(3
rt ) 2 u
-4
−
r -1 t
2 u 7
9 r 3
−
u 11
10.
m -
3 t -
5 −
( m
2 t 3 )
-1
1 −
mt 2
11. (
4 m 2 n
2 −
8 m
-1 �
) 0 1
12.
( -2m
n 2 )
-3
−
4 m -
6 n 4
-
m 3
−
32 n
10
7-2
Exam
ple
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NA
ME
DAT
E
P
ER
IOD
Lesson 7-2
Cha
pte
r 7
13
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceD
ivis
ion
Pro
pert
ies o
f E
xp
on
en
ts
Sim
pli
fy e
ach
exp
ress
ion
. Ass
um
e th
at n
o d
enom
inat
or e
qu
als
zero
.
1.
6 5 −
6 4 6
1 o
r 6
2.
9 12
−
9 8 94
or
6561
3.
x 4 −
x 2 x
2 4.
r 3 t
2 −
r 3 t
4 1 −
t 2
5.
m
−
m 3
1 −
m 2
6.
9 d 7
−
3 d 6 3
d
7.
12 n
5 −
36
n
n 4
−
3 8.
w
4 x 3
−
w 4 x
x
2
9.
a 3 b
5 −
ab
2 a
2 b3
10.
m 7 p
2 −
m
3 p 2 m
4
11.
-21
w 5 x
2 −
7 w
4 x 5
-
3w
−
x 3
12.
32 x 3 y
2 z 5
−
-8x
y z 2
-4x
2 yz
3
13.
( 4 p 7
−
7 r 2 ) 2
16 p
14
−
49 r 4
14. 4
-4
1 −
44 o
r
1 −
256
15. 8
-2
1 −
82 o
r 1 −
64
16.
( 5 −
3 ) -
2 9
−
25
17.
( 9 −
11 ) -
1 11
−
9 18
. h
3 −
h
-6 h
9
19. k
0 (k4 )
(k-
6 )
1 −
k 2
20. k
-1 (
ℓ-6 )
(m3 )
m
3 −
k �
6
21.
f -7
−
f 4
1 −
f 11
22.
( 16 p
5 w 2
−
2 p 3 w
3 ) 0 1
23.
f -5 g
4 −
h
-2
g 4 h
2 −
f 5
24.
15 x 6 y
-9
−
5xy -
11
3x
5 y2
25.
-15
t 0 u -
1 −
5 u
3 -
3 −
u 4
26.
48 x 6 y
7 z 5
−
-6x
y 5 z 6
-
8 x 5 y
2 −
z
7-2
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Answers (Lesson 7-2)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A5A01_A14_ALG1_A_CRM_C07_AN_660281.indd A5 12/20/10 7:11 PM12/20/10 7:11 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF 2nd
Chapter 7 A6 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
14
Gle
ncoe
Alg
ebra
1
Prac
tice
Div
isio
n P
rop
ert
ies o
f E
xp
on
en
ts
Sim
pli
fy e
ach
exp
ress
ion
. Ass
um
e th
at n
o d
enom
inat
or e
qu
als
zero
.
1.
8 8 −
8 4 8
4 o
r 40
96
2. a
4 b 6
−
ab 3
a3 b
3 3.
xy
2 −
xy
y
4.
m 5 n
p −
m
4 p
mn
5.
5 c
2 d 3
−
-4 c
2 d -
5 d 2
−
4 6.
8 y
7 z 6
−
4 y 6 z
5 2yz
7. ( 4f
3 g
−
3 h 6 ) 3
64 f 9 g
3 −
27 h
18
8. ( 6 w
5 −
7 p
6 r 3 ) 2
36 w
10
−
49 p
12 r 6
9.
-4 x
2 −
24
x 5 -
1 −
6 x 3
10. x
3 (y-
5 )(x
-8 )
1 −
x 5 y
5 11
. p(q
-2 )
(r-
3 )
p
−
q 2 r 3
12. 1
2-2
1
−
144
13. (
3 −
7 ) -
2 49
−
9 14
. ( 4 −
3 ) -
4 81
−
256
15.
22 r 3 s
2 −
11
r 2 s -
3 2rs
5
16.
-15
w 0 u
-1
−
5 u 3
-
3 −
u 4
17.
8 c 3 d
2 f 4
−
4 c -
1 d 2 f
-3 2
c4 f
7 18
. ( x -
3 y 5
−
4 -3 ) 0 1
19.
6 f -
2 g 3 h
5 −
54
f -2 g
-5 h
3 g
8 h 2
−
9
20.
-12
t -1 u
5 x -
4
−
2 t -
3 u x 5
-
6 t 2 u
4 −
x 9
21
.
r 4 −
(3
r ) 3
r −
27
22.
m -
2 n -
5 −
( m
4 n 3 )
-1
m 2
−
n 2
23.
( j -
1 k 3 )
-4
−
j 3 k 3
j −
k 15
24
. (2
a -
2 b ) -
3 −
5 a
2 b 4
a 4
−
40 b
7
25. ( q -
1 r 3
−
q r -
2 ) -5 q
10
−
r 25
26. (
7 c -
3 d 3
−
c 5 d h
-4 ) -
1 c
8 −
7 d 2 h
4 27
. ( 2 x 3 y
2 z
−
3 x 4 y
z -2 ) -
2 9 x
2 −
4 y 2 z
6
28. B
IOLO
GY
A l
ab t
ech
nic
ian
dra
ws
a sa
mpl
e of
blo
od. A
cu
bic
mil
lim
eter
of
the
bloo
d co
nta
ins
223
wh
ite
bloo
d ce
lls
and
225
red
bloo
d ce
lls.
Wh
at i
s th
e ra
tio
of w
hit
e bl
ood
cell
s to
red
blo
od c
ells
?
1 −
484
29. C
OU
NTI
NG
Th
e n
um
ber
of t
hre
e-le
tter
“w
ords
” th
at c
an b
e fo
rmed
wit
h t
he
En
glis
h
alph
abet
is
263 .
Th
e n
um
ber
of f
ive-
lett
er “
wor
ds”
that
can
be
form
ed i
s 26
5 . H
ow m
any
tim
es m
ore
five
-let
ter
“wor
ds”
can
be
form
ed t
han
th
ree-
lett
er “
wor
ds”?
676
7-2
001_
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AM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-2
Cha
pte
r 7
15
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
Div
isio
n P
rop
ert
ies o
f E
xp
on
en
ts
1. C
HEM
ISTR
Y T
he
nu
cleu
s of
a c
erta
in
atom
is
10-
13 c
enti
met
ers
acro
ss. I
f th
e n
ucl
eus
of a
dif
fere
nt
atom
is
10-
11 c
enti
met
ers
acro
ss, h
ow m
any
tim
es a
s la
rge
is i
t as
th
e fi
rst
atom
?
2. S
PAC
E T
he
Moo
n i
s ap
prox
imat
ely
254
kilo
met
ers
away
fro
m E
arth
on
av
erag
e. T
he
Oly
mpu
s M
ons
volc
ano
on
Mar
s st
ands
25
kilo
met
ers
hig
h. H
ow
man
y O
lym
pus
Mon
s vo
lcan
oes,
sta
cked
on
top
of
one
anot
her
, wou
ld f
it b
etw
een
th
e su
rfac
e of
th
e E
arth
an
d th
e M
oon
?
3. E
-MA
IL S
pam
(al
so k
now
n a
s ju
nk
e-m
ail)
con
sist
s of
ide
nti
cal
mes
sage
s se
nt
to t
hou
san
ds o
f e-
mai
l u
sers
. Peo
ple
ofte
n o
btai
n a
nti
-spa
m s
oftw
are
to f
ilte
r ou
t th
e ju
nk
e-m
ail
mes
sage
s th
ey
rece
ive.
Su
ppos
e Y
von
ne’
s an
ti-s
pam
so
ftw
are
filt
ered
ou
t 10
2 e-
mai
ls, a
nd
she
rece
ived
104
e-m
ails
las
t ye
ar. W
hat
fr
acti
on o
f h
er e
-mai
ls w
ere
filt
ered
ou
t?
Wri
te y
our
answ
er a
s a
mon
omia
l.
4. M
ETR
IC M
EASU
REM
ENT
Con
side
r a
dust
mit
e th
at m
easu
res
10-
3 m
illi
met
ers
in l
engt
h a
nd
a ca
terp
illa
r th
at m
easu
res
10 c
enti
met
ers
lon
g. H
ow m
any
tim
es a
s lo
ng
as t
he
mit
e is
th
e ca
terp
illa
r?
5. C
OM
PUTE
RS
In 1
995,
sta
nda
rd c
apac
ity
for
a pe
rson
al c
ompu
ter
har
d dr
ive
was
40
meg
abyt
es (
MB
). In
201
0, a
sta
nda
rd
har
d dr
ive
capa
city
was
500
gig
abyt
es
(GB
or
Gig
). R
efer
to
the
tabl
e be
low
.
Mem
ory
Cap
acit
y A
pp
roxi
mat
e C
onv
ersi
on
s
8 b
its =
1 b
yte
10
3 b
yte
s =
1 k
ilobyte
10
3 k
ilobyte
s =
1 m
ega
byte
(m
eg
)
10
3 m
ega
byte
s =
1 g
iga
byte
(g
ig)
10
3 g
iga
byte
s =
1 t
era
byte
10
3 t
era
byte
s =
1 p
eta
byte
a. T
he
new
er h
ard
driv
es h
ave
abou
t h
ow m
any
tim
es t
he
capa
city
of
the
1995
dri
ves?
b.
Pre
dict
th
e h
ard
driv
e ca
paci
ty i
n t
he
year
202
5 if
th
is r
ate
of g
row
th
con
tin
ues
.
c. O
ne
kilo
byte
of
mem
ory
is w
hat
fr
acti
on o
f on
e te
raby
te?
7-2
100
12,5
00
253 =
15,
625
10-
2
6.25
pet
abyt
es
1 −
109
= 1
0 -
9
104 =
10,
00
0
001_
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Answers (Lesson 7-2)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A6A01_A14_ALG1_A_CRM_C07_AN_660281.indd A6 12/24/10 9:29 AM12/24/10 9:29 AM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A7 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
16
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Patt
ern
s w
ith
Po
wers
Use
you
r ca
lcu
lato
r, if
nec
essa
ry, t
o co
mpl
ete
each
pat
tern
.
a. 2
10 =
b.
510 =
c.
410 =
2
9 =
59
=
49 =
2
8 =
58
=
48 =
2
7 =
57
=
47 =
2
6 =
56
=
46 =
2
5 =
55
=
45 =
2
4 =
54
=
44 =
2
3 =
53
=
43 =
2
2 =
52
=
42 =
2
1 =
51
=
41 =
Stu
dy
the
pat
tern
s fo
r a,
b, a
nd
c a
bov
e. T
hen
an
swer
th
e q
ues
tion
s.
1. D
escr
ibe
the
patt
ern
of
the
expo
nen
ts f
rom
th
e to
p of
eac
h c
olu
mn
to
the
bott
om.
Th
e ex
po
nen
ts d
ecre
ase
by o
ne
fro
m e
ach
ro
w t
o t
he
on
e b
elo
w.
2. D
escr
ibe
the
patt
e rn
of
the
pow
ers
from
th
e to
p of
th
e co
lum
n t
o th
e bo
ttom
. To
get
ea
ch p
ow
er, d
ivid
e th
e p
ow
er o
n t
he
row
ab
ove
by t
he
bas
e (2
, 5, o
r 4)
.
3. W
hat
wou
ld y
ou e
xpec
t th
e fo
llow
ing
pow
ers
to b
e?
20
1 50
1 40
1
4. R
efer
to
Exe
rcis
e 3.
Wri
te a
ru
le. T
est
it o
n p
atte
rns
that
you
obt
ain
usi
ng
22, 2
5, a
nd
24
as b
ases
.
Stu
dy
the
pat
tern
bel
ow. T
hen
an
swer
th
e q
ues
tion
s.
03 =
0
02 =
0
01 =
0
00 =
?
0-
1 do
es n
ot e
xist
. 0-
2 do
es n
ot e
xist
. 0-
3 do
es n
ot e
xist
.
5. W
hy
do 0
-1 ,
0-2 ,
and
0-3
not
exi
st?
Neg
ativ
e ex
po
nen
ts a
re n
ot
defi
ned
un
less
th
e b
ase
is n
on
zero
.
6. B
ased
upo
n t
he
patt
ern
, can
you
det
erm
ine
wh
eth
er 0
0 ex
ists
?
No
, sin
ce t
he
pat
tern
0n =
0 b
reak
s d
ow
n f
or
n <
1.
7. T
he
sym
bol
00 is
cal
led
an i
nd
eter
min
ate,
wh
ich
mea
ns
that
it
has
no
un
iqu
e va
lue.
T
hu
s it
doe
s n
ot e
xist
as
a u
niq
ue
real
nu
mbe
r. W
hy
do y
ou t
hin
k th
at 0
0 ca
nn
ot e
qual
1?
A
nsw
ers
will
var
y. O
ne
answ
er is
th
at if
00
= 1
, th
en 1
= 1 −
1 = 1
0 −
0 0 =
( 1 −
0 ) 0 ,
w
hic
h is
a f
alse
res
ult
, sin
ce d
ivis
ion
by
zero
is n
ot
allo
wed
. Th
us,
00
can
no
t eq
ual
1.
45
216
254
6412
58
256
625
1610
2431
2532
4096
15,6
2564
16,3
8478
,125
128
65,5
3639
0,62
525
626
2,14
41,
953,
125
512
1,04
8,57
69,
765,
625
7-2
1024
Any
no
nze
ro n
um
ber
to
th
e ze
ro p
ow
er e
qu
als
on
e.
001_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-3
Cha
pte
r 7
17
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
Rati
on
al
Exp
on
en
ts
Rat
ion
al E
xpo
nen
ts F
or a
ny
real
nu
mbe
rs a
an
d b
and
any
posi
tive
in
tege
r n
, if
an =
b, t
hen
a i
s an
nth
roo
t of
b. R
atio
nal
exp
onen
ts c
an b
e u
sed
to r
epre
sen
t n
th r
oots
.
Squ
are
Roo
t b
1 −
2 =
√ �
b
Cu
be R
oot
b 1 −
3 =
3 √ �
b
nth
Roo
t b
1 −
n =
n √ �
b
7-3
W
rite
(6x
y ) 1 −
2 in
rad
ical
fo
rm.
(6xy
) 1 −
2 =
√ �
�
6xy
Defi nitio
n o
f b
1
−
2
S
imp
lify
625
1 −
4 .
625 1
−
4 = 4 √
��
625
b 1
−
n =
n √
�
b
=
4 √ �
��
��
5 �
5 �
5 �
5
625 =
5 4
=
5
Sim
plif
y.
Exam
ple
1Ex
amp
le 2
Exer
cise
sW
rite
eac
h e
xpre
ssio
n i
n r
adic
al f
orm
, or
wri
te e
ach
rad
ical
in
exp
onen
tial
for
m.
1. 1
4 1 −
2 √
��
14
2.
5 x 1
−
2 5 √
�
x
3. 1
7 y 1 −
2 1
7 √
�
y
4. 1
2 1 −
2 √
��
12
5.
19 a
b 1 −
2 1
9a √
�
b
6.
√ �
�
17 1
7 1 −
2
7.
√ �
�
12n
(12
n ) 1
−
2 8.
√ �
�
18
b (1
8b ) 1
−
2 9.
√ �
�
37 3
7 1 −
2
Sim
pli
fy.
10.
3 √ �
�
343
7
11.
5 √ �
�
1024
4
12. 5
1 2 1 −
3 8
13.
4 √ �
�
2401
7
14.
6 √
��
64
2
15. 2
4 3 1 −
5 3
16.
3 √ �
�
1331
11
17.
4 √
��
�
6561
9
18. 4
09 6 1
−
4 8
001_
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PM
Answers (Lesson 7-2 and Lesson 7-3)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A7A01_A14_ALG1_A_CRM_C07_AN_660281.indd A7 12/20/10 7:11 PM12/20/10 7:11 PM
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
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cGraw
-Hill C
om
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PDF Pass
Chapter 7 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
18
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Rati
on
al
Exp
on
en
ts
7-3
Solv
e Ex
po
nen
tial
Eq
uat
ion
s In
an
exp
onen
tial
eq
uat
ion
, var
iabl
es o
ccu
r as
ex
pon
ents
. Use
th
e P
ower
Pro
pert
y of
Equ
alit
y an
d th
e ot
her
pro
pert
ies
of e
xpon
ents
to
solv
e ex
pon
enti
al e
quat
ion
s.
S
olve
102
4 x
− 1 =
4.
10
2 4 x
− 1 =
4
Ori
gin
al equation
( 4
5 ) x
− 1 =
4
Rew
rite
1024 a
s 4
5 .
4 5x
− 5 =
4 1
Pow
er
of
a P
ow
er,
Dis
trib
utive
Pro
pert
y
5x
− 5
= 1
P
ow
er
Pro
pert
y o
f E
qualit
y
5x
= 6
A
dd 5
to e
ach s
ide.
x =
6 −
5
Div
ide e
ach s
ide b
y 5
.
Exer
cise
sS
olve
eac
h e
qu
atio
n.
1. 2
x = 1
28 7
2.
3 3x
+ 1 =
81
1 3.
4 x
- 3 =
32
11
−
2
4. 5
x = 1
5,62
5 6
5. 6
3x +
2 =
216
1 −
3 6.
4 5x
- 3 =
16
1
7. 8
x = 4
096
4 8.
9 3x
+ 3 =
656
1 1 −
3 9.
1 1 x
- 1 =
133
1 4
10. 3
x = 6
561
8 11
. 2 5x
+ 4 =
512
1
12. 7
x -
2 =
343
5
13. 8
x = 2
62,1
44 6
14
. 5 5x
= 3
125
1 15
. 9 2x
- 6 =
656
1 5
16. 7
x = 2
401
4 17
. 7 3x
= 1
17,6
49 2
18
. 6 2x
- 7 =
777
6 6
19. 9
x = 7
29 3
20
. 8 3x
+ 1 =
409
6 1
21. 1
3 3x -
8 =
28,
561
4
Exam
ple
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-3
Cha
pte
r 7
19
Gle
ncoe
Alg
ebra
1
7-3
Skill
s Pr
acti
ceR
ati
on
al
Exp
on
en
tsW
rite
eac
h e
xpre
ssio
n i
n r
adic
al f
orm
, or
wri
te e
ach
rad
ical
in
exp
onen
tial
for
m.
1. (
8 x) 1
−
2 √ �
�
8x
2.
6z 1
−
2 6 √
�
z
3. √
��
19 1
9 1 −
2
4.
√ �
�
11 1
1 1 −
2 5.
19 x
1 −
2 1
9 √
�
x
6. √
��
34 3
4 1 −
2
7.
√ �
�
27g
(27g
) 1 −
2 8.
33 g
h 1 −
2 3
3g √
�
h
9.
√ �
��
13ab
c (1
3ab
c ) 1
−
2
Sim
pli
fy.
10. (
1 −
16 ) 1
−
4 1 −
2 11
. 5 √
��
3125
5
12. 7
2 9 1 −
3 9
13. (
1 −
32 ) 1
−
5 1 −
2 14
. 6 √
��
4096
4
15. 1
02 4 1
−
5 4
16. (
16
−
625 ) 1
−
4 2 −
5 17
. 6 √
��
�
15,6
25 5
18
. 117
,6 49
1 −
6 7
Sol
ve e
ach
eq
uat
ion
.
19. 2
x = 5
12 9
20
. 3 x =
656
1 8
21. 6
x = 4
6,65
6 6
22. 5
x = 1
25 3
23
. 3 x
- 3 =
243
8
24. 4
x -
1 =
102
4 6
25. 6
x -
1 =
129
6 5
26. 2
4x +
3 =
204
8 2
27. 3
3x +
3 =
656
1 5 −
3
001_
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Answers (Lesson 7-3)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A8A01_A14_ALG1_A_CRM_C07_AN_660281.indd A8 12/20/10 7:11 PM12/20/10 7:11 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A9 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
20
Gle
ncoe
Alg
ebra
1
7-3
Prac
tice
Rati
on
al
Exp
on
en
tsW
rite
eac
h e
xpre
ssio
n i
n r
adic
al f
orm
, or
wri
te e
ach
rad
ical
in
exp
onen
tial
for
m.
1.
√ �
�
13 1
3 1 −
2 2.
√ �
�
37 3
7 1 −
2 3.
√ �
�
17x
(17 x
) 1 −
2
4. (
7ab )
1 −
2 √ �
�
7a
b
5. 2
1z 1 −
2 2
1 √
�
z
6. 1
3(a b
) 1 −
2 1
3 √
��
ab
Sim
pli
fy.
7. (
1 −
81 ) 1
−
4 1 −
3 8.
5 √ �
�
1024
4
9. 5
1 2 1 −
3 8
10. (
32
−
1024
) 1 −
5 1
−
2 11
. 4 √
��
1296
6
12. 3
12 5 1
−
5 5
Sol
ve e
ach
eq
uat
ion
.
13. 3
x = 7
29 6
14
. 4 x =
409
6 6
15. 5
x = 1
5,62
5 6
16. 6
x +
3 =
777
6 2
17. 3
x -
3 =
218
7 10
18
. 4 3x
+ 4 =
16,
384
1
19. W
ATE
R T
he
flow
of
wat
er F
in
cu
bic
feet
per
sec
ond
over
a w
ier,
a sm
all
over
flow
dam
,
can
be
repr
esen
ted
by F
= 1
.26 H
3 −
2 ,
wh
ere
H i
s th
e h
eigh
t of
th
e w
ater
in
met
ers
abov
e th
e cr
est
of t
he
wie
r. F
ind
the
hei
ght
of t
he
wat
er i
f th
e fl
ow o
f th
e w
ater
is
10.0
8 cu
bic
feet
per
sec
ond.
4 f
t
001_
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Lesson X-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-3
Cha
pte
r 7
21
Gle
ncoe
Alg
ebra
1
7-3
Wor
d Pr
oble
m P
ract
ice
Rati
on
al
Exp
on
en
ts
1. V
ELO
CIT
Y T
he
velo
city
v i
n f
eet
per
seco
nd
of a
fre
ely
fall
ing
obje
ct t
hat
has
fa
llen
h f
eet
can
be
repr
esen
ted
by
v=
8 h
1 −
2 . F
ind
the
dist
ance
th
at a
n o
bjec
t h
as f
alle
n i
f it
s ve
loci
ty i
s 96
fee
t pe
r se
con
d. 1
44 f
t
2. E
LEC
TRIC
ITY
Th
e re
lati
onsh
ip o
f th
e cu
rren
t, t
he
pow
er, a
nd
the
resi
stan
ce
in a
n a
ppli
ance
can
be
mod
eled
by
I R 1 −
2 =
√ �
P
, w
her
e I
is t
he
curr
ent
in
ampe
res,
P i
s th
e po
wer
in
wat
ts, a
nd
R
is t
he
resi
stan
ce i
n o
hm
s. F
ind
the
pow
er
that
an
app
lian
ce i
s u
sin
g if
th
e cu
rren
t is
2.5
am
ps a
nd
the
resi
stan
ce i
s 16
oh
ms.
10
0 w
atts
3. G
EOM
ETRY
Th
e su
rfac
e ar
ea T
of
a cu
be i
n s
quar
e in
ches
can
be
dete
rmin
ed
by T
= 6
V 2 −
3 ,
wh
ere
V i
s th
e vo
lum
e of
the
cube
in
cu
bic
inch
es.
a. F
ind
the
surf
ace
area
of
a cu
be t
hat
h
as a
vol
um
e of
409
6 cu
bic
inch
es.
15
36 i n
2
b.
Fin
d th
e vo
lum
e of
a c
ube
th
at h
as a
su
rfac
e ar
ea o
f 96
squ
are
inch
es.
64
i n 3
4. P
LAN
ETS
Th
e av
erag
e di
stan
ce d
in
as
tron
omic
al u
nit
s th
at a
pla
net
is
from
the
Su
n c
an b
e m
odel
ed b
y d
=t 2
−
3 , w
her
e t
is t
he
nu
mbe
r of
Ear
th y
ears
th
at i
t ta
kes
for
the
plan
et t
o or
bit
the
Su
n.
a. F
ind
the
aver
age
dist
ance
a p
lan
et i
s fr
om t
he
Su
n i
f th
e pl
anet
has
an
or
bit
of 2
7 E
arth
yea
rs.
9 as
tro
no
mic
al u
nit
s
b.
Fin
d th
e ti
me
that
it
wou
ld t
ake
a pl
anet
to
orbi
t th
e S
un
if
its
aver
age
dist
ance
fro
m t
he
Su
n i
s 4
astr
onom
ical
un
its.
8
Ear
th y
ears
5. B
IOLO
GY
Th
e re
lati
onsh
ip b
etw
een
th
e m
ass
m i
n k
ilog
ram
s of
an
org
anis
m a
nd
its
met
abol
ism
P i
n C
alor
ies
per
day
can
be r
epre
sen
ted
by P
= 7
3.3
4 √ �
�
m 3
. Fin
d th
e m
ass
of a
n o
rgan
ism
th
at h
as a
m
etab
olis
m o
f 58
6.4
Cal
orie
s pe
r da
y.
16 k
g
6. M
AN
UFA
CTU
RIN
G T
he
prof
it P
of
a co
mpa
ny
in t
hou
san
ds o
f do
llar
s ca
n b
e
mod
eled
by
P =
12.
75 5 √
�
c 2 , w
her
e c
is t
he
nu
mbe
r of
cu
stom
ers
in h
un
dred
s. I
f th
e pr
ofit
of
the
com
pan
y is
$51
,000
, how
m
any
cust
omer
s do
th
ey h
ave?
320
0 cu
sto
mer
s
021_
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Answers (Lesson 7-3)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A9A01_A14_ALG1_A_CRM_C07_AN_660281.indd A9 12/20/10 7:12 PM12/20/10 7:12 PM
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
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cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 7 A10 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
22
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
7-3
Co
un
tere
xam
ple
sS
ome
stat
emen
ts i
n m
ath
emat
ics
can
be
prov
en f
alse
by
cou
nte
rexa
mp
les.
C
onsi
der
the
foll
owin
g st
atem
ent.
For
an
y n
um
bers
a a
nd
b, a
- b
= b
- a
.Yo
u c
an p
rove
th
at t
his
sta
tem
ent
is f
alse
in
gen
eral
if
you
can
fin
d on
e ex
ampl
e fo
r w
hic
h
the
stat
emen
t is
fal
se.
Let
a =
7 a
nd
b =
3. S
ubs
titu
te t
hes
e va
lues
in
th
e eq
uat
ion
abo
ve.
7 -
3 �
3 -
7
4 ≠
-4
In g
ener
al, f
or a
ny
nu
mbe
rs a
an
d b,
th
e st
atem
ent
a -
b =
b -
a i
s fa
lse.
You
can
mak
e th
e eq
uiv
alen
t ve
rbal
sta
tem
ent:
su
btra
ctio
n i
s n
ot a
com
mu
tati
ve o
pera
tion
.
In e
ach
of
the
foll
owin
g ex
erci
ses
a, b
, an
d c
are
an
y n
um
ber
s. P
rove
th
at t
he
stat
emen
t is
fal
se b
y co
un
tere
xam
ple
.
1. a
- (
b -
c)
� (
a -
b)
- c
2.
a ÷
(b
÷ c
) �
(a
÷ b
) ÷
c
3. a
÷ b
� b
÷ a
4.
a ÷
(b
+ c
) �
(a
÷ b
) +
(a
÷ c
)
5. a
1 −
2 +
a 1 −
2 � a
1 6.
a c �
b d �
(ab
) c +
d
7. W
rite
th
e ve
rbal
equ
ival
ents
for
Exe
rcis
es 1
, 2, a
nd
3.
8. F
or t
he
Dis
trib
uti
ve P
rope
rty
a(b
+ c
) =
ab
+ a
c, i
t is
sai
d th
at m
ult
ipli
cati
on
dist
ribu
tes
over
add
itio
n. E
xerc
ise
4 pr
oves
th
at s
ome
oper
atio
ns
do n
ot d
istr
ibu
te. W
rite
a
stat
emen
t fo
r th
e ex
erci
se t
hat
in
dica
tes
this
.
Sam
ple
an
swer
s ar
e g
iven
.
6
- (
4 -
2)
� (
6 -
4)
- 2
6 ÷
(4
÷ 2
) �
(6
÷ 4
) ÷
2
6
- 2
� 2
- 2
6 −
2 �
1.5
−
2
4
≠ 0
3
≠ 0
.75
6
÷ 4
� 4
÷ 6
6 ÷
(4
+ 2
) �
(6
÷ 4
) +
(6
÷ 2
)
3 −
2 ≠
2 −
3
6 ÷
6 �
1.5
+ 3
1
≠ 4
.5
9
1 −
2 + 9
1 −
2 � 9
1
2 3
� 5
2 �
[(2
)(5)
] (3 +
2)
3
+ 3
� 9
8 � 2
5 �
10
5
6
≠ 9
200
≠ 1
00,
00
0
1
. Su
btr
acti
on
is n
ot
an a
sso
ciat
ive
op
erat
ion
.
2. D
ivis
ion
is n
ot
an a
sso
ciat
ive
op
erat
ion
.
3. D
ivis
ion
is n
ot
a co
mm
uta
tive
op
erat
ion
.
4
. Div
isio
n d
oes
no
t d
istr
ibu
te o
ver
add
itio
n.
021_
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ALG
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-4
Cha
pte
r 7
23
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
Scie
nti
fi c N
ota
tio
n
7-4
Scie
nti
fic
No
tati
on
Ver
y la
rge
and
very
sm
all
nu
mbe
rs a
re o
ften
bes
t re
pres
ente
d u
sin
g a
met
hod
kn
own
as
scie
nti
fic
not
atio
n. N
um
bers
wri
tten
in
sci
enti
fic
not
atio
n t
ake
the
form
a ×
10
n, w
her
e 1
≤ a
< 1
0 a
nd
n i
s an
in
tege
r. A
ny
nu
mbe
r ca
n b
e w
ritt
en i
n
scie
nti
fic
not
atio
n.
E
xpre
ss 3
4,02
0,00
0,00
0 in
sc
ien
tifi
c n
otat
ion
.S
tep
1
Mov
e th
e de
cim
al p
oin
t u
nti
l it
is
to t
he
righ
t of
th
e fi
rst
non
zero
dig
it. T
he
resu
lt i
s a
real
nu
mbe
r a.
Her
e, a
= 3
.402
.
Ste
p 2
N
ote
the
nu
mbe
r of
pla
ces
n a
nd
the
dire
ctio
n t
hat
you
mov
ed t
he
deci
mal
po
int.
Th
e de
cim
al p
oin
t m
oved
10
plac
es t
o th
e le
ft, s
o n
= 1
0.
Ste
p 3
B
ecau
se t
he
deci
mal
mov
ed t
o th
e le
ft, w
rite
th
e n
um
ber
as a
× 1
0n.
34,0
20,0
00,0
00 =
3.4
0200
0000
0 ×
1010
Ste
p 4
Rem
ove
the
extr
a ze
ros.
3.4
02 ×
1010
E
xpre
ss 4
.11
× 1
0-6 in
st
and
ard
not
atio
n.
Ste
p 1
T
he
expo
nen
t is
–6,
so
n =
–6.
Ste
p 2
B
ecau
se n
< 0
, mov
e th
e de
cim
al
poin
t 6
plac
es t
o th
e le
ft.
4.
11 ×
10
-6 ⇒
.0
00
00
41
1
Ste
p 3
4.
11 ×
10
-6 ⇒
0.0
00
00
41
1R
ew
rite
; in
sert
a 0
befo
re t
he d
ecim
al poin
t.
Exam
ple
1Ex
amp
le 2
Exer
cise
sE
xpre
ss e
ach
nu
mb
er i
n s
cien
tifi
c n
otat
ion
.
1. 5
,100
,000
2.
80,
300,
000,
000
3. 1
4,25
0,00
0
5.1
× 1
06 8
.03
× 1
010
1.4
25 ×
107
4. 6
8,07
0,00
0,00
0,00
0 5.
14,
000
6. 9
01,0
50,0
00,0
00
6.8
07 ×
1013
1
.4 ×
104
9.0
105
× 1
011
7. 0
.004
9 8.
0.0
0030
1 9.
0.0
0000
0051
9
4.9
× 1
0-3
3.0
1 ×
10-
4 5
.19
× 1
0-8
10. 0
.000
0001
85
11. 0
.002
002
12. 0
.000
0077
1
1.8
5 ×
10-
7 2
.002
× 1
0-3
7.7
1 ×
10-
6
Exp
ress
eac
h n
um
ber
in
sta
nd
ard
for
m.
13. 4
.91
× 1
04 14
. 3.2
× 1
0-5
15. 6
.03
× 1
08
4
9,10
0 0
.00
003
2 6
03,0
00,
00
0
16. 2
.001
× 1
0-6
17. 1
.000
24 ×
1010
18
. 5 ×
105
0
.00
00
020
01
10,
002
,40
0,0
00
50
0,0
00
19. 9
.09
× 1
0-5
20. 3
.5 ×
10-
2 21
. 1.7
087
× 1
07
0
.00
009
09
0.0
35
17,
087,
00
0
021_
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Answers (Lesson 7-3 and Lesson 7-4)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A10A01_A14_ALG1_A_CRM_C07_AN_660281.indd A10 12/20/10 7:12 PM12/20/10 7:12 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
24
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Scie
nti
fi c N
ota
tio
n
7-4
Pro
du
cts
and
Qu
oti
ents
in S
cien
tifi
c N
ota
tio
n Y
ou c
an u
se s
cien
tifi
c n
otat
ion
to
sim
plif
y m
ult
iply
ing
and
divi
din
g ve
ry l
arge
an
d ve
ry s
mal
l n
um
bers
.
E
valu
ate
(9.2
× 1
0-3 )
×(4
× 1
08 ). E
xpre
ss t
he
resu
lt i
n b
oth
sc
ien
tifi
c n
otat
ion
an
d s
tan
dar
d f
orm
.
(9.2
× 1
0-3 )
(4 ×
108 )
O
rigin
al expre
ssio
n
= (
9.2
× 4
)(10
-3
× 1
08 )
Com
muta
tive
and
Associa
tive
Pro
pert
ies
=
36.
8 ×
105
Pro
duct
of
Pow
ers
=
(3.
68 ×
101 )
× 1
05 36.8
= 3
.68 ×
10
=
3.6
8 ×
106
Pro
duct
of
Pow
ers
=
3,6
80,0
00
Sta
ndard
Form
E
valu
ate
( 2.7
6 ×
1
0 7
) −
( 6.9
× 1
0 5
) .
Exp
ress
th
e re
sult
in
bot
h s
cien
tifi
c n
otat
ion
an
d s
tan
dar
d f
orm
. ( 2
.76
× 1
0 7 )
−
( 6.9
× 1
0 5 )
=
( 2.76
−
6.9 ) (
10 7
−
10 5 )
Product
rule
for
fractions
= 0
.4 ×
102
Quotient
of
Pow
ers
= 4
.0 ×
10-
1 ×
102
0.4
= 4
.0 ×
10
-1
= 4
.0 ×
101
Pro
duct
of
Pow
ers
= 4
0 S
tandard
form
Exam
ple
1Ex
amp
le 2
Exer
cise
sE
valu
ate
each
pro
du
ct. E
xpre
ss t
he
resu
lts
in b
oth
sci
enti
fic
not
atio
n a
nd
st
and
ard
for
m.
1. (
3.4
× 1
03 )(5
× 1
04 )
2. (2
.8 ×
10-
4 )(1
.9 ×
107 )
1
.7 ×
108 ;
170
,00
0,0
00
5.3
2 ×
103 ;
532
0
3. (
6.7
× 1
0-7 )
(3 ×
103 )
4.
(8.1
× 1
05 )(2
.3 ×
10-
3 )
2.0
1 ×
10-
3 ; 0
.002
01
1.8
63 ×
103 ;
186
3
5. (
1.2
× 1
0 -4 )
2 6.
(5.9
× 1
0 5 ) 2
1
.44
× 1
0 -
8 ; 0
.00
00
00
0144
3
.481
× 1
0 11
; 34
8,10
0,0
00,
00
0
Eva
luat
e ea
ch q
uot
ien
t. E
xpre
ss t
he
resu
lts
in b
oth
sci
enti
fic
not
atio
n a
nd
st
and
ard
for
m.
7.
( 4.9
× 1
0 -
3 )
−
( 2.5
× 1
0 -
4 )
8.
5.8
× 1
0 4
−
5 ×
10
-2
1
.96
× 1
01 ; 1
9.6
1.1
6 ×
106 ;
1,1
60,0
00
9.
( 1.6
× 1
0 5 )
−
( 4 ×
1 0
-4 )
10
. 8.
6 ×
10 6
−
1.6
× 1
0 -3
4
.0 ×
108 ;
40
0,0
00,
00
0 5
.375
× 1
09 ; 5
,375
,00
0,0
00
11.
( 4.2
× 1
0 -
2 )
−
( 6 ×
1 0
-7 )
12
. 8.
1 ×
10 5
−
2.7
× 1
0 4
7
× 1
04 ; 7
0,0
00
3 ×
101 ;
30
021_
040_
ALG
1_A
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M_C
07_C
R_6
6028
1.in
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/20/
10
6:38
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-4
Cha
pte
r 7
25
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceS
cie
nti
fi c N
ota
tio
n
7-4
Exp
ress
eac
h n
um
ber
in
sci
enti
fic
not
atio
n.
1. 3
,400
,000
,000
2.
0.0
0000
0312
3
.4 ×
109
3.1
2 ×
10-
7
3. 2
,091
,000
4.
980
,200
,000
,000
,000
2
.091
× 1
06 9
.802
× 1
014
5. 0
.000
0000
0008
6.
0.0
0142
8
× 1
0-11
1
.42
× 1
0-3
Exp
ress
eac
h n
um
ber
in
sta
nd
ard
for
m.
7. 2
.1 ×
105
8. 8
.023
× 1
0-7
2
10,0
00
0.0
00
00
0802
3
9. 3
.63
× 1
0-6
10. 7
.15
× 1
08
0
.00
00
0363
7
15,0
00,
00
0
11. 1
.86
× 1
0-4
12. 4
.9 ×
105
0
.00
0186
4
90,0
00
Eva
luat
e ea
ch p
rod
uct
. Exp
ress
th
e re
sult
s in
bot
h s
cien
tifi
c n
otat
ion
an
d
stan
dar
d f
orm
.
13. (
6.1
× 1
05 )(2
× 1
05 )
14. (
4.4
× 1
06 )(1
.6 ×
10-
9 )
1.2
2 ×
1011
; 12
2,0
00,
00
0,0
00
7.0
4 ×
10-
3 ; 0
.007
04
15. (
8.8
× 1
08 )(3
.5 ×
10-
13)
16. (
1.35
× 1
08 )(7
.2 ×
10-
4 )
3.0
8 ×
10-
4 ; 0
.00
0308
9
.72
× 1
04 ; 9
7,20
0
17. (
2.2
× 1
0 -3 ) 2
18. (
3.4
× 1
0 2 ) 2
4
.84
× 1
0 -
6 ; 0
.00
00
0484
1
.156
× 1
0 5 ;
115
,60
0
Eva
luat
e ea
ch q
uot
ien
t. E
xpre
ss t
he
resu
lts
in b
oth
sci
enti
fic
not
atio
n a
nd
st
and
ard
for
m.
19. (9
.2 ×
10-
8 )
−
(2
× 1
0-6 )
20
. (4
.8 ×
104 )
−
(3 ×
10-
5 )
4
.6 ×
10-
2 ; 0
.046
1
.6 ×
109 ;
1,6
00,
00
0,0
00
21.
(1.1
61 ×
10-
9 )
−
(4.3
× 1
0-6 )
22.
( 4.6
25 ×
1 0 1
0 )
−
( 1.2
5 ×
10 4
)
2
.7 ×
10-
4 ; 0
.00
027
3.7
× 1
06 ; 3
,70
0,0
00
23.
(2.3
76 ×
10-
4 )
−
(7.2
× 1
0-8 )
24.
(8.7
4 ×
10-
3 )
−
(1
.9 ×
105 )
3
.3 ×
103 ;
3,3
00
4.6
× 1
0-8 ;
0.0
00
00
004
6
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Answers (Lesson 7-4)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A11A01_A14_ALG1_A_CRM_C07_AN_660281.indd A11 12/20/10 7:12 PM12/20/10 7:12 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 7 A12 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
26
Gle
ncoe
Alg
ebra
1
Prac
tice
Scie
nti
fi c N
ota
tio
n
7-4
Exp
ress
eac
h n
um
ber
in
sci
enti
fic
not
atio
n.
1. 1
,900
,000
2.
0.0
0070
4
1.9
× 10
6
7.0
4 ×
10-
4
3. 5
0,04
0,00
0,00
0 4.
0.0
0000
0066
1
5.0
04 ×
1010
6
.61
× 1
0-8
Exp
ress
eac
h n
um
ber
in
sta
nd
ard
for
m.
5. 5
.3 ×
107
6. 1
.09
× 1
0-4
5
3,0
00,
00
0 0
.00
0109
7. 9
.13
× 1
03 8.
7.9
02 ×
10-
6
9
130
0.0
00
007
902
Eva
luat
e ea
ch p
rod
uct
. Exp
ress
th
e re
sult
s in
bot
h s
cien
tifi
c n
otat
ion
an
d
stan
dar
d f
orm
.
9. (
4.8
× 1
04 )(6
× 1
06 )
10. (
7.5
× 1
0-5 )
(3.2
× 1
07 )
2.8
8 ×
1011
; 28
8,0
00,
00
0,0
00
2.4
× 1
03 ; 2
400
11. (
2.06
× 1
04 )(5
.5 ×
10-
9 )
12. (
8.1
× 1
0-6 )
(1.9
6 ×
1011
)
1.1
33 ×
10-
4 ; 0
.00
0113
3 1
.587
6 ×
106 ;
1,5
87,6
00
13. (
7.2
× 1
0 -5 )
2 14
. (5.
29 ×
1 0 6 )
2
5.1
84 ×
1 0
-9 ;
0.0
00
00
00
0518
4 2.
7984
1 ×
10
13 ;
27,9
84,1
00,
00
0,0
00
Eva
luat
e ea
ch q
uot
ien
t. E
xpre
ss t
he
resu
lts
in b
oth
sci
enti
fic
not
atio
n a
nd
st
and
ard
for
m.
15.
(4.2
× 1
0 5 )
−
(3 ×
1 0 -
3 )
16.
(1.7
6 ×
1 0 -
11 )
−
(2.2
× 1
0 -5 )
1
.4 ×
108 ;
140
,00
0,0
00
8 ×
10-
7 ; 0
.00
00
008
17.
(7.0
5 ×
1 0 12
)
−
(9.4
× 1
0 7 )
18.
(2.0
4 ×
1 0 -
4 )
−
(3
.4 ×
1 0 5 )
7
.5 ×
104 ;
75,
00
0 6
× 1
0-10
; 0.
00
00
00
00
06
19. G
RA
VIT
ATI
ON
Iss
ac N
ewto
n’s
th
eory
of
un
iver
sal
grav
itat
ion
sta
tes
that
th
e eq
uat
ion
F
= G
m1m
2 −
r2
can
be
use
d to
cal
cula
te t
he
amou
nt
of g
ravi
tati
onal
for
ce i
n n
ewto
ns
betw
een
tw
o po
int
mas
ses
m1
and
m2
sepa
rate
d by
a d
ista
nce
r. G
is
a co
nst
ant
equ
al
to 6
.67
× 1
0-
11 N
m2 k
g–2 .
Th
e m
ass
of E
arth
m1
is e
qual
to
5.97
× 1
02
4 k
g, t
he
mas
s of
th
e M
oon
m2
is e
qual
to
7.36
× 1
022 k
g, a
nd
the
dist
ance
r b
etw
een
th
e tw
o is
384
,000
,000
m.
a. E
xpre
ss t
he
dist
ance
r i
n s
cien
tifi
c n
otat
ion
. 3.
84 ×
108
m
b.
Com
pute
th
e am
oun
t of
gra
vita
tion
al f
orce
bet
wee
n E
arth
an
d th
e M
oon
. Exp
ress
yo
ur
answ
er i
n s
cien
tifi
c n
otat
ion
. 1.
99 ×
1020
New
ton
s
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10
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-4
Cha
pte
r 7
27
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
Scie
nti
fi c N
ota
tio
n
7-4
1. P
LAN
ETS
Nep
tun
e’s
mea
n d
ista
nce
fro
m
the
Su
n i
s 4,
500,
000,
000
kilo
met
ers.
U
ran
us’
mea
n d
ista
nce
fro
m t
he
Su
n i
s 2,
870,
000,
000
kilo
met
ers.
Exp
ress
th
ese
dist
ance
s in
sci
enti
fic
not
atio
n.
N
eptu
ne:
4.5
× 1
09km
; U
ran
us:
2.
87 ×
109
km
2. P
ATH
OLO
GY
Th
e co
mm
on c
old
is
cau
sed
by t
he
rhin
ovir
us,
wh
ich
co
mm
only
mea
sure
s 2
× 1
0-
8 m
in
di
amet
er. T
he
E. c
oli
bact
eriu
m, w
hic
h
cau
ses
food
poi
son
ing,
com
mon
ly
mea
sure
s 3
× 1
0-
6 m
in
len
gth
. Exp
ress
th
ese
mea
sure
men
ts i
n s
tan
dard
for
m.
R
hin
ovir
us:
0.0
00
00
002
m;
E. c
oli:
0.
00
00
03 m
3. C
OM
MER
CIA
LS A
30-
seco
nd
com
mer
cial
air
ed d
uri
ng
the
2007
Su
per
Bow
l co
st $
2,60
0,00
0. A
30-
seco
nd
com
mer
cial
air
ed d
uri
ng
the
1967
Su
per
Bow
l co
st $
40,0
00. E
xpre
ss t
hes
e va
lues
in
sci
enti
fic
not
atio
n. H
ow m
any
tim
es
mor
e ex
pen
sive
was
it
to a
ir a
n
adve
rtis
emen
t du
rin
g th
e 20
07 S
upe
r B
owl
than
th
e 19
67 S
upe
r B
owl?
20
07 S
up
er B
ow
l: $
2.6
× 10
6 ; 1
967
Su
per
Bo
wl:
$ 4
× 1
04 ;
6.5
× 1
01 o
r 65
tim
es m
ore
ex
pen
sive
4. A
VO
GA
DR
O’S
NU
MB
ER A
voga
dro’
s n
um
ber
is a
n i
mpo
rtan
t co
nce
pt i
n
chem
istr
y. I
t st
ates
th
at t
he
nu
mbe
r 6.
022
× 1
02
3 i
s ap
prox
imat
ely
equ
al t
o th
e n
um
ber
of m
olec
ule
s in
12
gram
s of
ca
rbon
12.
Use
Avo
gadr
o’s
nu
mbe
r to
de
term
ine
the
nu
mbe
r of
mol
ecu
les
in
5 ×
10
-7 g
ram
s of
car
bon
12.
2.
509
× 1
016 m
ole
cule
s
5. C
OA
L R
ESER
VES
Th
e ta
ble
belo
w s
how
s th
e n
um
ber
of k
ilog
ram
s of
coa
l se
lect
co
un
trie
s h
ad i
n p
rove
n r
eser
ve a
t th
e en
d of
a r
ecen
t ye
ar.
Co
al R
eser
ves
Co
un
try
Co
al (
kg)
Un
ite
d S
tate
s2
.46
× 1
014
Ru
ssia
1.5
7 ×
10
14
Ind
ia9
.24
× 1
013
Ro
ma
nia
4.9
4 ×
10
11
Sour
ce: B
ritis
h Pe
trol
eum
a. E
xpre
ss e
ach
cou
ntr
y’s
coal
res
erve
s in
sta
nda
rd f
orm
. U
nit
ed S
tate
s:
246,
00
0,0
00,
00
0,0
00
kg;
Ru
ssia
: 15
7,0
00,
00
0,0
00,
00
0 kg
; In
dia
: 92
,40
0,0
00,
00
0,0
00
kg;
Ro
man
ia:
494,
00
0,0
00,
00
0 kg
b.
How
man
y ti
mes
mor
e co
al d
oes
the
Un
ited
Sta
tes
hav
e th
an R
oman
ia?
4.98
× 1
02 o
r 49
8 ti
mes
c. O
ne
kilo
gram
of
coal
has
an
en
ergy
de
nsi
ty o
f 2.
4 ×
10
7 jo
ule
s. W
hat
is
the
tota
l en
ergy
den
sity
of
the
Un
ited
S
tate
s’ c
oal
rese
rve?
Exp
ress
you
r an
swer
in
sci
enti
fic
not
atio
n.
5.
90 ×
1021
jou
les
021_
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Answers (Lesson 7-4)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A12A01_A14_ALG1_A_CRM_C07_AN_660281.indd A12 12/20/10 7:12 PM12/20/10 7:12 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A13 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
28
Gle
ncoe
Alg
ebra
1
7-4
Enri
chm
ent
En
gin
eeri
ng
No
tati
on
En
gin
eeri
ng
not
atio
n i
s a
vari
atio
n o
n s
cien
tifi
c n
otat
ion
wh
ere
nu
mbe
rs a
re e
xpre
ssed
as
pow
ers
of 1
000
rath
er t
han
as
pow
ers
of 1
0. E
ngi
nee
rin
g n
otat
ion
tak
es t
he
fam
ilia
r fo
rm
of a
× 1
0n, b
ut
n i
s re
stri
cted
to
mu
ltip
les
of t
hre
e an
d 1
≤ |
a|<
1000
.O
ne
adva
nta
ge t
o en
gin
eeri
ng
not
atio
n i
s th
at n
um
bers
can
be
nea
tly
expr
esse
d u
sin
g S
I pr
efix
es. T
hes
e pr
efix
es a
re t
ypic
ally
use
d fo
r sc
ien
tifi
c m
easu
rem
ents
.
100
0n10
nS
I Pre
fi x
Sym
bo
l10
00
510
15
pe
taP
10
00
410
12
tera
T
10
00
310
9g
iga
G
10
00
210
6m
ega
M
10
00
110
3kilo
k
10
00
-1
10
-3
mill
im
10
00
-2
10
-6
mic
roμ
10
00
-3
10
-9
na
no
n
10
00
-4
10
-12
pic
op
10
00
-5
10
-15
fem
tof
N
UC
LEA
R P
OW
ER T
he
outp
ut
of a
nu
clea
r p
ower
pla
nt
is m
easu
red
to
be
620,
000,
000
wat
ts. E
xpre
ss t
his
nu
mb
er i
n e
ngi
nee
rin
g n
otat
ion
an
d u
sin
g S
I p
refi
xes.
To
expr
ess
a n
um
ber
in e
ngi
nee
rin
g n
otat
ion
, fir
st c
onve
rt t
he
nu
mbe
r to
sci
enti
fic
not
atio
n.
Ste
p 1
62
0,00
0,00
0 ⇒
6.2
0000
000
a =
6.2
0000000
Ste
p 2
T
he
deci
mal
poi
nt
mov
ed 8
pla
ces
to t
he
left
, so
n =
8.
Ste
p 3
62
0,00
0,00
0 =
6.2
0000
000
× 1
08 =
6.2
× 1
08
Bec
ause
8 i
s n
ot a
mu
ltip
le o
f 3,
we
nee
d to
rou
nd
dow
n n
to
the
nex
t m
ult
iple
of
3.
Ste
p 4
6.
2 ×
108
= (
6.2
× 1
02 ) ×
106
620 =
6.2
× 1
02
Ste
p 5
=
620
× 1
06 P
roduct
of
Pow
ers
Th
e ou
tpu
t of
th
e po
wer
pla
nt
is 6
20 ×
106
wat
ts. U
sin
g th
e ch
art
abov
e, t
he
pref
ix f
or 1
06 is
fou
nd
to b
e m
ega,
or
M. T
he
outp
ut
of t
he
pow
er p
lan
t is
620
meg
awat
ts, o
r 62
0MW
.
Exer
cise
sE
xpre
ss e
ach
nu
mb
er i
n e
ngi
nee
rin
g n
otat
ion
.
1. 4
0,00
0,00
0,00
0 40
× 1
09 2.
180
,000
,000
,000
,000
180
× 1
012
3. 0
.000
06 6
0 ×
10-
6 4.
0.0
0000
0000
0003
9 39
0 ×
10-
15
Exp
ress
eac
h m
easu
rem
ent
usi
ng
SI
pre
fixe
s.
5. 0
.000
0000
0014
gra
m
6. 4
0,00
0,00
0,00
0 w
atts
1
40 p
ico
gra
ms
(pg
) 4
0 g
igaw
atts
(G
W)
7. 6
3,10
0,00
0,00
0,00
0 by
tes
8. 0
.000
0002
met
er
63.
1 te
raby
tes
(TB
) 2
00
nan
om
eter
s (n
m)
Exam
ple
021_
040_
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-5
Cha
pte
r 7
29
Gle
ncoe
Alg
ebra
1
7-5
Gra
ph
Exp
on
enti
al F
un
ctio
ns
Exp
on
enti
al F
un
ctio
na
fu
nctio
n d
efi n
ed
by a
n e
qu
atio
n o
f th
e fo
rm y
= a
bx ,
wh
ere
a ≠
0,
b >
0,
an
d b
≠ 1
You
can
use
val
ues
of
x to
fin
d or
dere
d pa
irs
that
sat
isfy
an
exp
onen
tial
fu
nct
ion
. Th
en y
ou
can
use
th
e or
dere
d pa
irs
to g
raph
th
e fu
nct
ion
.
G
rap
h y
= 3
x . F
ind
th
e y-
inte
rcep
t an
d s
tate
th
e d
omai
n a
nd
ra
nge
.
xy
-2
1
−
9
-1
1
−
3
01
13
29
Th
e y-
inte
rcep
t is
1.
Th
e do
mai
n i
s al
l re
al n
um
bers
, an
d th
e ra
nge
is
all
posi
tive
nu
mbe
rs.x
y
O
G
rap
h y
= (
1 −
4 ) x . Fin
d t
he
y-in
terc
ept
and
sta
te t
he
dom
ain
an
d
ran
ge.
Th
e y-
inte
rcep
t is
1.
Th
e do
mai
n i
s al
l re
al n
um
bers
, an
d th
e ra
nge
is
all
pos
itiv
e n
um
bers
.
x
y
O2
8
Exer
cise
sG
rap
h e
ach
fu
nct
ion
. Fin
d t
he
y-in
terc
ept
and
sta
te t
he
dom
ain
an
d r
ange
.
1. y
= 0
.3x
2. y
= 3
x +
1
3. y
= ( 1
−
3 ) x + 1
x
y
O1
2
x
y
O2
16 4812
x
y
O1
2
1
; D
= {
all r
eal
2; D
= {
all r
eal
2;
D =
{al
l rea
ln
um
ber
s},
nu
mb
ers}
,
nu
mb
ers}
,R
= {
y|y >
0}
R =
{y
|y >
1}
R
= {
y|y >
1}
Exam
ple
1Ex
amp
le 2
xy
-2
16
-1
4
01
1 1
−
4
2 1
−
16
Stud
y G
uide
and
Inte
rven
tion
Exp
on
en
tial
Fu
ncti
on
s
021_
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ALG
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PM
Answers (Lesson 7-4 and Lesson 7-5)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A13A01_A14_ALG1_A_CRM_C07_AN_660281.indd A13 12/20/10 7:12 PM12/20/10 7:12 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF 2nd
Chapter 7 A14 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
30
Gle
ncoe
Alg
ebra
1
7-5
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Exp
on
en
tial
Fu
ncti
on
s
Iden
tify
Exp
on
enti
al B
ehav
ior
It i
s so
met
imes
use
ful
to k
now
if
a se
t of
dat
a is
ex
pon
enti
al. O
ne
way
to
tell
is
to o
bser
ve t
he
shap
e of
th
e gr
aph
. An
oth
er w
ay i
s to
obs
erve
th
e pa
tter
n i
n t
he
set
of d
ata.
D
eter
min
e w
het
her
th
e se
t of
dat
a sh
own
bel
ow d
isp
lays
ex
pon
enti
al b
ehav
ior.
Wri
te y
es o
r n
o. E
xpla
in w
hy
or w
hy
not
.
Met
hod
1: L
ook
for
a P
atte
rnT
he
dom
ain
val
ues
in
crea
se b
y re
gula
r in
terv
als
of 2
, wh
ile
the
ran
ge v
alu
es h
ave
a co
mm
on f
acto
r of
1 −
2 .
Sin
ce t
he
dom
ain
va
lues
in
crea
se b
y re
gula
r in
terv
als
and
the
ran
ge v
alu
es h
ave
a co
mm
on f
acto
r, th
e da
ta a
re p
roba
bly
expo
nen
tial
.
Met
hod
2: G
raph
th
e D
ata
T
he
grap
h s
how
s ra
pidl
y de
crea
sin
g va
lues
of
y as
x
incr
ease
s. T
his
is
char
acte
rist
ic o
f ex
pon
enti
al
beh
avio
r.
Exer
cise
s
Det
erm
ine
wh
eth
er t
he
set
of d
ata
show
n b
elow
dis
pla
ys e
xpon
enti
al b
ehav
ior.
W
rite
yes
or
no.
Exp
lain
wh
y or
wh
y n
ot.
1.
x0
12
3
y5
10
15
20
2.
x
01
23
y3
92
78
1
N
o;
the
do
mai
n v
alu
es a
re a
t re
gu
lar
Yes
; th
e d
om
ain
val
ues
are
at
inte
rval
s, a
nd
th
e ra
ng
e va
lues
hav
e r
egu
lar
inte
rval
s, a
nd
th
e ra
ng
e a
com
mo
n d
iffer
ence
5.
val
ues
hav
e a
com
mo
n f
acto
r 3.
3.
x-
11
35
y3
216
84
4.
x
-1
01
23
y3
33
33
Y
es;
the
do
mai
n v
alu
es a
re a
t
No
; th
e d
om
ain
val
ues
are
at
reg
ula
r in
terv
als,
an
d t
he
ran
ge
r
egu
lar
inte
rval
s, b
ut
the
ran
ge
valu
es h
ave
a co
mm
on
fac
tor
1 −
2 . v
alu
es d
o n
ot
chan
ge.
5.
x-
50
510
y1
0.5
0.2
50
.12
5
6.
x
01
23
4
y 1
−
3
1
−
9
1
−
27
1
−
81
1
−
24
3
Y
es;
the
do
mai
n v
alu
es a
re a
t
Yes
; th
e d
om
ain
val
ues
are
at
reg
ula
r in
terv
als,
an
d t
he
ran
ge
r
egu
lar
inte
rval
s, a
nd
th
e ra
ng
e va
lues
hav
e a
com
mo
n f
acto
r 0.
5.
val
ues
hav
e a
com
mo
n f
acto
r 1 −
3 .
Exam
ple
x0
24
68
10
y6
43
216
84
2
x
y
O4
8
16324872
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10
8:22
AM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-5
Cha
pte
r 7
31
Gle
ncoe
Alg
ebra
1
7-5
Skill
s Pr
acti
ceE
xp
on
en
tial
Fu
ncti
on
s
Gra
ph
eac
h f
un
ctio
n. F
ind
th
e y-
inte
rcep
t, a
nd
sta
te t
he
dom
ain
an
d r
ange
.
1. y
= 2
x 2.
y =
( 1 −
3 ) x
1
; D
= {
all r
eal n
um
ber
s},
1
; D
= {
all r
eal n
um
ber
s},
R =
{y |
y >
0}
R
= {
y |
y >
0}
3. y
= 3
(2x )
4.
y =
3x +
2
3;
D =
{al
l rea
l nu
mb
ers}
,
3; D
= {
all r
eal n
um
ber
s},
R
= {
y |
y >
0}
R
= {
y |
y >
2}
Det
erm
ine
wh
eth
er t
he
set
of d
ata
show
n b
elow
dis
pla
ys e
xpon
enti
al b
ehav
ior.
W
rite
yes
or
no.
Exp
lain
wh
y or
wh
y n
ot.
5.
x-
3-
2-
10
y9
12
15
18
6.
x
05
10
15
y2
010
52
.5
N
o;
the
do
mai
n v
alu
es a
re a
t
Yes
; th
e d
om
ain
val
ues
are
at
reg
ula
r in
terv
als
and
th
e ra
ng
e
reg
ula
r in
terv
als
and
th
e ra
ng
e va
lues
hav
e a
com
mo
n
val
ues
hav
e a
com
mo
n f
acto
r 0.
5.d
iffer
ence
3.
7.
x4
812
16
y2
04
08
016
0
8.
x
50
30
10
-10
y9
07
05
03
0
Y
es;
the
do
mai
n v
alu
es a
re a
t
No
; th
e d
om
ain
val
ues
are
at
reg
ula
r in
terv
als
and
th
e ra
ng
e
reg
ula
r in
terv
als
and
th
e ra
ng
e va
lues
hav
e a
com
mo
n f
acto
r 2.
v
alu
es h
ave
a co
mm
on
d
iffer
ence
20.x
y
Ox
y
O
x
y
Ox
y
O
021_
040_
ALG
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_CR
M_C
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6:39
PM
Answers (Lesson 7-5)
A01_A14_ALG1_A_CRM_C07_AN_660281.indd A14A01_A14_ALG1_A_CRM_C07_AN_660281.indd A14 12/24/10 9:28 AM12/24/10 9:28 AM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A15 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
32
Gle
ncoe
Alg
ebra
1
7-5
Prac
tice
E
xp
on
en
tial
Fu
ncti
on
sG
rap
h e
ach
fu
nct
ion
. Fin
d t
he
y-in
terc
ept
and
sta
te t
he
dom
ain
an
d r
ange
.
1. y
= (
1 −
10 ) x
2. y
= 3
x 3.
y =
( 1 −
4 ) x
4. y
= 4
(2x )
+ 1
5.
y =
2(2
x - 1
)
6. y
= 0
.5(3
x - 3
)
Det
erm
ine
wh
eth
er t
he
set
of d
ata
show
n b
elow
dis
pla
ys e
xpon
enti
al b
ehav
ior.
W
rite
yes
or
no.
Exp
lain
wh
y or
wh
y n
ot.
7.
x2
58
11
y4
80
12
03
07.
5
8.
x
21
18
15
12
y3
02
316
9
Y
es;
the
do
mai
n v
alu
es a
re a
t
No
; th
e d
om
ain
val
ues
are
at
reg
ula
r in
terv
als
and
th
e ra
ng
e
reg
ula
r in
terv
als
and
th
e ra
ng
eva
lues
hav
e a
com
mo
n
val
ues
hav
e a
com
mo
n
fact
or
0.25
. d
iffer
ence
7.
9. L
EAR
NIN
G M
s. K
lem
pere
r to
ld h
er E
ngl
ish
cla
ss t
hat
eac
h w
eek
stu
den
ts t
end
to f
orge
t on
e si
xth
of
the
voca
bula
ry w
ords
th
ey l
earn
ed t
he
prev
iou
s w
eek.
Su
ppos
e a
stu
den
t le
arn
s 60
wor
ds. T
he
nu
mbe
r of
wor
ds r
emem
bere
d ca
n b
e de
scri
bed
by t
he
fun
ctio
n
W
(x)
= 6
0 ( 5 −
6 ) x , w
her
e x
is t
he
nu
mbe
r of
wee
ks t
hat
pas
s. H
ow m
any
wor
ds w
ill
the
s
tude
nt
rem
embe
r af
ter
3 w
eeks
? ab
ou
t 35
10. B
IOLO
GY
Su
ppos
e a
cert
ain
cel
l re
prod
uce
s it
self
in
fou
r h
ours
. If
a la
b re
sear
cher
be
gin
s w
ith
50
cell
s, h
ow m
any
cell
s w
ill
ther
e be
aft
er o
ne
day,
tw
o da
ys, a
nd
thre
e da
ys?
(Hin
t: U
se t
he
expo
nen
tial
fu
nct
ion
y =
50(
2x ).)
32
00
cells
; 20
4,80
0 ce
lls;
13,1
07,2
00
cells
x
y
Ox
y
O
x
y
O
x
y
Ox
y
Ox
y
O
1; D
= {
all r
eal
nu
mb
ers}
;
R =
{ y
| y
> 0}
1; D
= {
all r
eal
nu
mb
ers}
;
R =
{ y
| y
> 0}
1; D
= {
all r
eal
num
bers
};
R =
{ y
| y
> 0}
5; D
= {
all
real
nu
mb
ers}
; R
= {
y |
y >
1}
0; D
= {
all
real
nu
mb
ers}
; R
= {
y |
y >
-2}
-1;
D =
{a
ll re
al
num
bers
};
R =
{ y
| y >
-1.
5}
021_
040_
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M_C
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R_6
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7 -5
Cha
pte
r 7
33
Gle
ncoe
Alg
ebra
1
7-5
1. W
AST
E S
upp
ose
the
was
te g
ener
ated
by
non
recy
cled
pap
er a
nd
card
boar
d pr
odu
cts
is a
ppro
xim
ated
by
the
foll
owin
g fu
nct
ion
.y
= 1
000(
2)0.
3x
Ske
tch
th
e ex
pon
enti
al f
un
ctio
n o
n t
he
coor
din
ate
grid
bel
ow. y
xO950
650
350
1850
1550
2450
2150
1250
43
21
-2-
1-
3-
4
2. M
ON
EY T
atya
na’
s gr
andf
ath
er g
ave
her
on
e pe
nn
y on
th
e da
y sh
e w
as b
orn
. He
plan
s to
dou
ble
the
amou
nt
he
give
s h
er
ever
y da
y. E
stim
ate
how
mu
ch s
he
wil
l re
ceiv
e fr
om h
er g
ran
dfat
her
on
th
e 12
th
day
of h
er l
ife.
abo
ut
$20
3.PI
CTU
RE
FRA
MES
Sin
ce a
pic
ture
fra
me
incl
ude
s a
bord
er, t
he
pict
ure
mu
st b
e sm
alle
r in
are
a th
an
the
enti
re f
ram
e. T
he
tabl
e sh
ows
the
rela
tion
ship
bet
wee
n
pict
ure
are
a an
d fr
ame
len
gth
for
a p
arti
cula
r li
ne
of f
ram
es. I
s th
is
an e
xpon
enti
al
rela
tion
ship
? E
xpla
in.
No
; th
ere
is n
o c
om
mo
n f
acto
r b
etw
een
th
e p
ictu
re a
reas
.
4.D
EPR
ECIA
TIO
N T
he
valu
e of
Roy
ce
Com
pan
y’s
com
pute
r eq
uip
men
t is
de
crea
sin
g in
val
ue
acco
rdin
g to
th
e fo
llow
ing
fun
ctio
n.
y=
400
0(0.
87)x
In t
he
equ
atio
n, x
is
the
nu
mbe
r of
ye
ars
that
hav
e el
apse
d si
nce
th
e eq
uip
men
t w
as p
urc
has
ed a
nd
y is
th
e va
lue
in d
olla
rs. W
hat
was
th
e va
lue
5 ye
ars
afte
r it
was
pu
rch
ased
? R
oun
d yo
ur
answ
er t
o th
e n
eare
st d
olla
r.$1
994
5. M
ETEO
RO
LOG
Y T
he
atm
osph
eric
pr
essu
re i
n m
illi
bars
at
alti
tude
x
met
ers
can
be
appr
oxim
ated
by
the
foll
owin
g fu
nct
ion
. Th
e fu
nct
ion
is
vali
d fo
r va
lues
of
x be
twee
n 0
an
d 10
,000
.
f (
x) =
103
8(1.
0001
34)-
x
a.
Wh
at i
s th
e pr
essu
re a
t se
a le
vel?
10
38 m
illib
ars
b
. T
he
McD
onal
d O
bser
vato
ry i
n T
exas
is
at
an a
ltit
ude
of
2000
met
ers.
Wh
at
is t
he
appr
oxim
ate
atm
osph
eric
pr
essu
re t
her
e?
794
mill
ibar
s
c.
As
alti
tude
in
crea
ses,
wh
at h
appe
ns
to
atm
osph
eric
pre
ssu
re?
It
dec
reas
es.
Wor
d Pr
oble
m P
ract
ice
Exp
on
en
tial
Fu
ncti
on
s
Sid
e P
ictu
re L
eng
th
Are
a (
in.)
(i
n2 )
5
6
6
12
7
2
0
8
3
0
9
4
2
021_
040_
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10
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PM
Answers (Lesson 7-5)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A15A15_A26_ALG1_A_CRM_C07_AN_660281.indd A15 12/20/10 7:11 PM12/20/10 7:11 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 7 A16 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
34
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Lo
gari
thm
ic F
un
cti
on
s
7-5
You
hav
e fo
un
d th
e in
vers
e of
a l
inea
r fu
nct
ion
by
inte
rch
angi
ng
x an
d y
in t
he
equ
atio
n o
f th
e fu
nct
ion
. Th
e in
vers
e of
an
exp
onen
tial
fu
nct
ion
is
call
ed a
log
arit
hm
ic f
un
ctio
n.
F
ind
th
e in
vers
e fu
nct
ion
of
the
exp
onen
tial
fu
nct
ion
y =
2x .
Mak
e a
tab
le o
f va
lues
for
eac
h f
un
ctio
n. T
hen
gra
ph
bot
h f
un
ctio
ns.
To
fin
d th
e in
vers
e fu
nct
ion
, in
terc
han
ge x
an
d y.
Th
e in
vers
e of
y =
2 x i
s x
= 2
y .
y =
2 x
x =
2 y
xy
xy
-3
1
−
8
1
−
8
-3
-2
1
−
4
1
−
4
-2
-1
1
−
2
1
−
2
-1
0
11
0
1
22
1
2
44
2
3
88
3
In g
ener
al t
he
inve
rse
of y
= b
x is
x =
b y .
In x
= b
y , th
e va
riab
le y
is
call
ed t
he
loga
rith
m
of x
. Th
is i
s u
sual
ly w
ritt
en a
s y
= l
o g b
x.
Exer
cise
s
1. W
hat
are
th
e do
mai
n a
nd
ran
ge o
f y
= l
o g 2
x? H
ow a
re t
he
dom
ain
an
d ra
nge
rel
ated
to
the
dom
ain
an
d ra
nge
of
y =
2 x ?
D =
{x
|x >
0},
R =
{al
l rea
l nu
mb
ers}
; Th
e d
om
ain
of
y =
lo g
2 x is
th
e ra
ng
e o
f y =
2 x a
nd
th
e ra
ng
e o
f y =
lo g
2 x is
th
e d
om
ain
of
y =
2 x .
2. H
ow a
re t
he
grap
hs
of y
= l
o g 2
x an
d y
= 2
x rel
ated
?
Th
ey a
re r
efl e
ctio
ns
in t
he
line
y =
x.
3. T
hro
ugh
wh
ich
qu
adra
nts
do
the
grap
hs
of y
= l
o g 2
x an
d y
= 2
x pas
s?
y =
lo g
2 x p
asse
s th
rou
gh
I an
d II
; y =
2 x p
asse
s th
rou
gh
I an
d IV
.
4. I
f an
exp
onen
tial
fu
nct
ion
fin
ds p
opu
lati
on a
s a
fun
ctio
n o
f ti
me,
wh
at c
an y
ou c
oncl
ude
ab
out
its
inve
rse
loga
rith
mic
fu
nct
ion
? T
he
log
arit
hm
ic f
un
ctio
n fi
nd
s ti
me
as a
fu
nct
ion
of
po
pu
lati
on
.
5. R
ESEA
RC
H I
nve
stig
ate
real
-wor
ld u
ses
of l
ogar
ith
mic
fu
nct
ion
s. H
ow a
re l
ogar
ith
mic
fu
nct
ion
s u
sed
to m
odel
rea
l-w
orld
sit
uat
ion
s?S
amp
le a
nsw
er: T
he
Ric
hte
r sc
ale
is a
log
arit
hm
ic f
un
ctio
n u
sed
to
m
easu
re e
arth
qu
ake
inte
nsi
ty.
Exam
ple
y
xO12
812
8 4
4
y =
x
y =
2x
x =
2y
021_
040_
ALG
1_A
_CR
M_C
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R_6
6028
1.in
dd
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10
6:39
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-6
Cha
pte
r 7
35
Gle
ncoe
Alg
ebra
1
7-6
Stud
y G
uide
and
Inte
rven
tion
Gro
wth
an
d D
ecay
Exp
on
enti
al G
row
th P
opu
lati
on i
ncr
ease
s an
d gr
owth
of
mon
etar
y in
vest
men
ts a
re
exam
ples
of
exp
onen
tial
gro
wth
. Th
is m
ean
s th
at a
n i
nit
ial
amou
nt
incr
ease
s at
a s
tead
y ra
te o
ver
tim
e.
Th
e g
en
era
l e
qu
atio
n fo
r exp
on
en
tia
l gro
wth
is y
= a
(1 +
r)t .
• y
rep
rese
nts
th
e fi n
al a
mo
un
t.
Exp
on
enti
al G
row
th
•
a re
pre
se
nts
th
e in
itia
l a
mo
un
t.
• r
rep
rese
nts
th
e r
ate
of
ch
an
ge
exp
resse
d a
s a
de
cim
al.
• t
rep
rese
nts
tim
e.
POPU
LATI
ON
Th
e p
opu
lati
on o
f Jo
hn
son
Cit
y in
200
5 w
as
25,0
00. S
ince
th
en, t
he
pop
ula
tion
has
gr
own
at
an a
vera
ge r
ate
of 3
.2%
eac
h y
ear.
a. W
rite
an
eq
uat
ion
to
rep
rese
nt
the
pop
ula
tion
of
Joh
nso
n C
ity
sin
ce 2
005.
Th
e ra
te 3
.2%
can
be
wri
tten
as
0.03
2.y
= a
(1 +
r)t
y =
25,
000(
1 +
0.0
32)t
y =
25,
000(
1.03
2)t
b.
Acc
ord
ing
to t
he
equ
atio
n, w
hat
wil
l th
e p
opu
lati
on o
f J
ohn
son
Cit
y b
e in
201
5?
In 2
015
t w
ill
equ
al 2
015
- 2
005
or 1
0.S
ubs
titu
te 1
0 fo
r t
in t
he
equ
atio
n f
rom
pa
rta.
y =
25,
000(
1.03
2)10
t=
10
≈
34,
256
In 2
015
the
popu
lati
on o
f Jo
hn
son
Cit
y w
ill
be a
bou
t 34
,256
.
INV
ESTM
ENT
Th
e G
arci
as h
ave
$12,
000
in a
sav
ings
ac
cou
nt.
Th
e b
ank
pay
s 3.
5% i
nte
rest
on
sav
ings
acc
oun
ts, c
omp
oun
ded
m
onth
ly. F
ind
th
e b
alan
ce i
n 3
yea
rs.
Th
e ra
te 3
.5%
can
be
wri
tten
as
0.03
5.
Th
e sp
ecia
l eq
uat
ion
for
com
pou
nd
inte
rest
is
A=
P (1
+r − n
)nt , w
her
e A
repr
esen
ts t
he
bala
nce
, P i
s th
e in
itia
l am
oun
t, r
rep
rese
nts
th
e an
nu
al r
ate
expr
esse
d as
a d
ecim
al, n
rep
rese
nts
th
e n
um
ber
of t
imes
th
e in
tere
st i
s co
mpo
un
ded
each
yea
r, an
d t
repr
esen
ts
the
nu
mbe
r of
yea
rs t
he
mon
ey i
s in
vest
ed.
A=
P (1
+r − n
)nt
= 1
2,00
0 (1
+
0.03
5−
12)3(
12)
≈ 1
3,32
6.49
In t
hre
e ye
ars,
th
e ba
lan
ce o
f th
e ac
cou
nt
wil
l be
$13
,326
.49.
Exer
cise
s 1
. PO
PULA
TIO
N T
he
popu
lati
on o
f th
e U
nit
ed
2. IN
VES
TMEN
T D
eter
min
e th
e S
tate
s h
as b
een
in
crea
sin
g at
an
ave
rage
v
alu
e of
an
in
vest
men
t of
$25
00
ann
ual
rat
e of
0.9
1%. I
f th
e po
pula
tion
was
i
f it
is
inve
sted
at
an i
nte
rest
rat
e of
ab
out
303,
146,
000
in 2
008,
pre
dict
th
e
5.2
5% c
ompo
un
ded
mon
thly
for
po
pula
tion
in
201
2.
4
yea
rs.
$308
2.78
abo
ut
314,
332,
051
3. P
OPU
LATI
ON
It
is e
stim
ated
th
at t
he
4.
INV
ESTM
ENT
Det
erm
ine
the
popu
lati
on o
f th
e w
orld
is
incr
easi
ng
at
val
ue
of a
n i
nve
stm
ent
of $
100,
000
an
ave
rage
an
nu
al r
ate
of 1
.3%
. If
the
i
f it
is
inve
sted
at
an i
nte
rest
rat
e of
20
08 p
opu
lati
on w
as a
bou
t 6,
641,
000,
000,
5.2
% c
ompo
un
ded
quar
terl
y fo
r
pred
ict
the
2015
pop
ula
tion
.
12
year
s.
abou
t 7,
269,
417,
259
$
185,
888.
87
Exam
ple
1Ex
amp
le 2
021_
040_
ALG
1_A
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M_C
07_C
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dd
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10
6:39
PM
Answers (Lesson 7-5 and Lesson 7-6)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A16A15_A26_ALG1_A_CRM_C07_AN_660281.indd A16 12/20/10 7:11 PM12/20/10 7:11 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A17 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
36
Gle
ncoe
Alg
ebra
1
7-6
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Gro
wth
an
d D
ecay
Exp
on
enti
al D
ecay
Rad
ioac
tive
dec
ay a
nd
depr
ecia
tion
are
exa
mpl
es o
f ex
pon
enti
al
dec
ay. T
his
mea
ns
that
an
in
itia
l am
oun
t de
crea
ses
at a
ste
ady
rate
ove
r a
peri
od o
f ti
me.
Th
e g
en
era
l e
qu
atio
n fo
r exp
on
en
tia
l d
ecay is y
= a
(1 -
r)t .
• y
rep
rese
nts
th
e fi n
al a
mo
un
t.
Exp
on
enti
al D
ecay
•
a re
pre
se
nts
th
e in
itia
l a
mo
un
t.
• r
rep
rese
nts
th
e r
ate
of
de
cay e
xp
resse
d a
s a
de
cim
al.
• t
rep
rese
nts
tim
e.
D
EPR
ECIA
TIO
N T
he
orig
inal
pri
ce o
f a
trac
tor
was
$45
,000
. Th
e va
lue
of t
he
trac
tor
dec
reas
es a
t a
stea
dy
rate
of
12%
per
yea
r.
a. W
rite
an
eq
uat
ion
to
rep
rese
nt
the
valu
e of
th
e tr
acto
r si
nce
it
was
pu
rch
ased
.
Th
e ra
te 1
2% c
an b
e w
ritt
en a
s 0.
12.
y =
a(1
- r
)t G
enera
l equation for
exponential decay
y =
45,
000(
1 -
0.1
2)t
a =
45,0
00 a
nd r
= 0
.12
y =
45,
000(
0.88
)t S
implif
y.
b.
Wh
at i
s th
e va
lue
of t
he
trac
tor
in 5
yea
rs?
y =
45,
000(
0.88
)t E
quation for
decay f
rom
part
a
y =
45,
000(
0.88
)5 t
= 5
y ≈
23,
747.
94
Use a
calc
ula
tor.
In 5
yea
rs, t
he
trac
tor
wil
l be
wor
th a
bou
t $2
3,74
7.94
.
Exer
cise
s 1
. PO
PULA
TIO
N T
he
popu
lati
on o
f B
ulg
aria
has
bee
n d
ecre
asin
g at
an
an
nu
al
rate
of
0.89
%. I
f th
e po
pula
tion
of
Bu
lgar
ia w
as a
bou
t 7,
450,
349
in t
he
year
20
05, p
redi
ct i
ts p
opu
lati
on i
n t
he
year
201
5. a
bo
ut
6,81
3,20
4
2. D
EPR
ECIA
TIO
N M
r. G
osse
ll i
s a
mac
hin
ist.
He
bou
ght
som
e n
ew m
ach
iner
y fo
r ab
out
$125
,000
. He
wan
ts t
o ca
lcu
late
th
e va
lue
of t
he
mac
hin
ery
over
th
e n
ext
10 y
ears
for
ta
x pu
rpos
es. I
f th
e m
ach
iner
y de
prec
iate
s at
th
e ra
te o
f 15
% p
er y
ear,
wh
at i
s th
e va
lue
of t
he
mac
hin
ery
(to
the
nea
rest
$10
0) a
t th
e en
d of
10
year
s? a
bo
ut
$24,
600
3. A
RC
HA
EOLO
GY
Th
e h
alf-
life
of
a ra
dioa
ctiv
e el
emen
t is
def
ined
as
the
tim
e th
at i
t ta
kes
for
one-
hal
f a
quan
tity
of
the
elem
ent
to d
ecay
. Rad
ioac
tive
car
bon
-14
is f
oun
d in
al
l li
vin
g or
gan
ism
s an
d h
as a
hal
f-li
fe o
f 57
30 y
ears
. Con
side
r a
livi
ng
orga
nis
m w
ith
an
or
igin
al c
once
ntr
atio
n o
f ca
rbon
-14
of 1
00 g
ram
s.
a. I
f th
e or
gan
ism
liv
ed 5
730
year
s ag
o, w
hat
is
the
con
cen
trat
ion
of
carb
on-1
4 to
day?
50
gb
. If
th
e or
gan
ism
liv
ed 1
1,46
0 ye
ars
ago,
det
erm
ine
the
con
cen
trat
ion
of
carb
on-1
4 to
day.
25
g
4. D
EPR
ECIA
TIO
N A
new
car
cos
ts $
32,0
00. I
t is
exp
ecte
d to
dep
reci
ate
12%
eac
h y
ear
for
4 ye
ars
and
then
dep
reci
ate
8% e
ach
yea
r th
erea
fter
. Fin
d th
e va
lue
of t
he
car
in
6 ye
ars.
ab
ou
t $1
6,24
2.63
Exam
ple
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-6
Cha
pte
r 7
37
Gle
ncoe
Alg
ebra
1
7-6
Skill
s Pr
acti
ceG
row
th a
nd
Decay
1. P
OPU
LATI
ON
Th
e po
pula
tion
of
New
Yor
k C
ity
incr
ease
d fr
om 8
,008
,278
in
200
0 to
8,1
68,3
88 i
n 2
005.
Th
e an
nu
al r
ate
of p
opu
lati
on i
ncr
ease
for
th
e pe
riod
was
ab
out
0.4%
.
a. W
rite
an
equ
atio
n f
or t
he
popu
lati
on t
yea
rs a
fter
200
0. P
= 8
,008
,278
(1.0
04)t
b.
Use
th
e eq
uat
ion
to
pred
ict
the
popu
lati
on o
f N
ew Y
ork
Cit
y in
201
5.
abo
ut
8,50
2,46
5
2. S
AV
ING
S T
he
Fre
sh a
nd
Gre
en C
ompa
ny
has
a s
avin
gs p
lan
for
its
em
ploy
ees.
If
an
empl
oyee
mak
es a
n i
nit
ial
con
trib
uti
on o
f $1
000,
th
e co
mpa
ny
pays
8%
in
tere
st
com
pou
nde
d qu
arte
rly.
a. I
f an
em
ploy
ee p
arti
cipa
tin
g in
th
e pl
an w
ith
draw
s th
e ba
lan
ce o
f th
e ac
cou
nt
afte
r 5
year
s, h
ow m
uch
wil
l be
in
th
e ac
cou
nt?
$14
85.9
5
b.
If a
n e
mpl
oyee
par
tici
pati
ng
in t
he
plan
wit
hdr
aws
the
bala
nce
of
the
acco
un
t af
ter
35 y
ears
, how
mu
ch w
ill
be i
n t
he
acco
un
t? $
15,9
96.4
7
3. H
OU
SIN
G M
r. an
d M
rs. B
oyce
bou
ght
a h
ouse
for
$96
,000
in
199
5. T
he
real
est
ate
brok
er i
ndi
cate
d th
at h
ouse
s in
th
eir
area
wer
e ap
prec
iati
ng
at a
n a
vera
ge a
nn
ual
rat
e of
7%
. If
the
appr
ecia
tion
rem
ain
ed s
tead
y at
th
is r
ate,
wh
at w
as t
he
valu
e of
th
e B
oyce
’s h
ome
in 2
009?
ab
ou
t $2
47,5
39
4. M
AN
UFA
CTU
RIN
G Z
elle
r In
dust
ries
bou
ght
a pi
ece
of w
eavi
ng
equ
ipm
ent
for
$60,
000.
It
is
expe
cted
to
depr
ecia
te a
t an
ave
rage
rat
e of
10%
per
yea
r.
a. W
rite
an
equ
atio
n f
or t
he
valu
e of
th
e pi
ece
of e
quip
men
t af
ter
t ye
ars.
E
= 6
0,0
00(
0.90
)t
b.
Fin
d th
e va
lue
of t
he
piec
e of
equ
ipm
ent
afte
r 6
year
s. a
bo
ut
$31,
886
5. F
INA
NC
ES K
yle
save
d $5
00 f
rom
a s
um
mer
job.
He
plan
s to
spe
nd
10%
of
his
sav
ings
ea
ch w
eek
on v
ario
us
form
s of
en
tert
ain
men
t. A
t th
is r
ate,
how
mu
ch w
ill
Kyl
e h
ave
left
af
ter
15 w
eeks
? $1
02.9
5
6. T
RA
NSP
OR
TATI
ON
Tif
fan
y’s
mot
her
bou
ght
a ca
r fo
r $9
000
five
yea
rs a
go. S
he
wan
ts
to s
ell
it t
o T
iffa
ny
base
d on
a 1
5% a
nn
ual
rat
e of
dep
reci
atio
n. A
t th
is r
ate,
how
mu
ch
wil
l Tif
fan
y pa
y fo
r th
e ca
r? a
bo
ut
$399
3
021_
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Answers (Lesson 7-6)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A17A15_A26_ALG1_A_CRM_C07_AN_660281.indd A17 12/20/10 7:11 PM12/20/10 7:11 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF 2nd
Chapter 7 A18 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
38
Gle
ncoe
Alg
ebra
1
7-6
Prac
tice
G
row
th a
nd
Decay
1.C
OM
MU
NIC
ATI
ON
S S
port
s ra
dio
stat
ion
s n
um
bere
d 22
0 in
199
6. T
he
nu
mbe
r of
sp
orts
rad
io s
tati
ons
has
sin
ce i
ncr
ease
d by
app
roxi
mat
ely
14.3
% p
er y
ear.
a. W
rite
an
equ
atio
n f
or t
he
nu
mbe
r of
spo
rts
radi
o st
atio
ns
for
t ye
ars
afte
r 19
96.
R=
220
(1.1
43)t
b.
If t
he
tren
d co
nti
nu
es, p
redi
ct t
he
nu
mbe
r of
spo
rts
radi
o st
atio
ns
in 2
015.
ab
ou
t 27
88 s
tati
on
s
2. I
NV
ESTM
ENTS
Det
erm
ine
the
amou
nt
of a
n i
nve
stm
ent
if $
500
is i
nve
sted
at
an
inte
rest
rat
e of
4.2
5% c
ompo
un
ded
quar
terl
y fo
r 12
yea
rs.
$830
.41
3. I
NV
ESTM
ENTS
Det
erm
ine
the
amou
nt
of a
n i
nve
stm
ent
if $
300
is i
nve
sted
at
an
inte
rest
rat
e of
6.7
5% c
ompo
un
ded
sem
ian
nu
ally
for
20
year
s.
$113
1.73
4. H
OU
SIN
G T
he
Gre
ens
bou
ght
a co
ndo
min
ium
for
$11
0,00
0 in
201
0. I
f it
s va
lue
appr
ecia
tes
at a
n a
vera
ge r
ate
of 6
% p
er y
ear,
wh
at w
ill
the
valu
e be
in
201
5?
abo
ut
$147
,205
5. D
EFO
RES
TATI
ON
Du
rin
g th
e 19
90s,
th
e fo
rest
ed a
rea
of G
uat
emal
a de
crea
sed
at a
n
aver
age
rate
of
1.7%
.
a. I
f th
e fo
rest
ed a
rea
in G
uat
emal
a in
199
0 w
as a
bou
t 34
,400
squ
are
kilo
met
ers,
wri
te
an
equ
atio
n f
or t
he
fore
sted
are
a fo
r t
year
s af
ter
1990
. C
= 3
4,40
0(0.
983)
t
b.
If t
his
tre
nd
con
tin
ues
, pre
dict
th
e fo
rest
ed a
rea
in 2
015.
abo
ut
22,4
07.6
5 km
2
6. B
USI
NES
S A
pie
ce o
f m
ach
iner
y va
lued
at
$25,
000
depr
ecia
tes
at a
ste
ady
rate
of
10%
yea
rly.
Wh
at w
ill
the
valu
e of
th
e pi
ece
of m
ach
iner
y be
aft
er 7
yea
rs?
abo
ut
$11,
957
7. T
RA
NSP
OR
TATI
ON
A n
ew c
ar c
osts
$18
,000
. It
is e
xpec
ted
to d
epre
ciat
e at
an
ave
rage
ra
te o
f 12
% p
er y
ear.
Fin
d th
e va
lue
of t
he
car
in 8
yea
rs.
abo
ut
$647
3
8. P
OPU
LATI
ON
Th
e po
pula
tion
of
Osa
ka, J
apan
, dec
lin
ed a
t an
ave
rage
an
nu
al r
ate
of 0
.05%
for
th
e fi
ve y
ears
bet
wee
n 1
995
and
2000
. If
the
popu
lati
on o
f O
saka
was
11
,013
,000
in
200
0 an
d it
con
tin
ues
to
decl
ine
at t
he
sam
e ra
te, p
redi
ct t
he
popu
lati
on
in 2
050.
ab
ou
t 10
,741
,021
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AM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-6
Cha
pte
r 7
39
Gle
ncoe
Alg
ebra
1
7-6
1. D
EPR
ECIA
TIO
N T
he
valu
e of
a n
ew
plas
ma
tele
visi
on d
epre
ciat
es b
y ab
out
7% e
ach
yea
r. A
eryn
pu
rch
ases
a 5
0-in
ch
plas
ma
tele
visi
on f
or $
3000
. Wh
at i
s it
s va
lue
afte
r 4
year
s? R
oun
d yo
ur
answ
er
to t
he
nea
rest
hu
ndr
ed.
abo
ut
$220
0
2. M
ON
EY H
ans
open
s a
savi
ngs
acc
oun
t by
dep
osit
ing
$120
0 in
an
acc
oun
t th
at
earn
s 3
perc
ent
inte
rest
com
pou
nde
d w
eekl
y. H
ow m
uch
wil
l h
is i
nve
stm
ent
be
wor
th i
n 1
0 ye
ars?
Ass
um
e th
at t
her
e ar
e ex
actl
y 52
wee
ks i
n a
yea
r an
d ro
un
d yo
ur
answ
er t
o th
e n
eare
st c
ent.
$1
619.
69
3. H
IGH
ER E
DU
CA
TIO
N T
he
tabl
e li
sts
the
aver
age
cost
s of
att
endi
ng
a fo
ur-
year
co
lleg
e in
th
e U
nit
ed S
tate
s du
rin
g a
rece
nt
year
.
S
ourc
e: C
olle
ge B
oard
Ru
ss’s
par
ents
in
vest
ed m
oney
in
a
savi
ngs
acc
oun
t ea
rnin
g an
ave
rage
of
4.5
perc
ent
inte
rest
, com
pou
nde
d m
onth
ly.
Aft
er 1
5 ye
ars,
th
ey h
ave
exac
tly
the
righ
t am
oun
t to
cov
er t
he
tuit
ion
, fee
s,
room
an
d bo
ard
for
Ru
ss’s
fir
st y
ear
at a
pu
blic
col
lege
. Wh
at w
as t
hei
r in
itia
l in
vest
men
t? R
oun
d yo
ur
answ
er t
o th
e n
eare
st d
olla
r. $6
182
4.PO
PULA
TIO
N I
n 2
007
the
U.S
. Cen
sus
Bu
reau
est
imat
ed t
he
popu
lati
on o
f th
e U
nit
ed S
tate
s es
tim
ated
at
301
mil
lion
. T
he
ann
ual
rat
e of
gro
wth
is
abou
t 0.
89%
. At
this
rat
e, w
hat
is
the
expe
cted
po
pula
tion
at
the
tim
e of
th
e 20
20
cen
sus?
Rou
nd
you
r an
swer
to
the
nea
rest
ten
mil
lion
.
340
mill
ion
5. M
EDIC
INE
Wh
en d
octo
rs p
resc
ribe
m
edic
atio
n, t
hey
hav
e to
con
side
r th
e ra
te a
t w
hic
h t
he
body
fil
ters
a d
rug
from
th
e bl
oods
trea
m. S
upp
ose
it t
akes
th
e h
um
an b
ody
6 da
ys t
o fi
lter
ou
t h
alf
of
the
Flu
-B-G
one
vacc
ine.
Th
e am
oun
t of
F
lu-B
-Gon
e va
ccin
e re
mai
nin
g in
th
e bl
oods
trea
m x
day
s af
ter
an i
nje
ctio
n i
s
giv
en b
y th
e eq
uat
ion
y =
y0 (
0.5)
x −
6 , w
her
e y 0
is t
he
init
ial
amou
nt.
Su
ppos
e a
doct
or
inje
cts
a pa
tien
t w
ith
20
μg
(mic
rogr
ams)
of
Flu
-B-G
one.
a. H
ow m
uch
of
the
vacc
ine
wil
l re
mai
n
afte
r 1
day?
Rou
nd
you
r an
swer
to
the
nea
rest
ten
th.
17
.8 μ
g
b.
How
mu
ch o
f th
e va
ccin
e w
ill
rem
ain
af
ter
12 d
ays?
Rou
nd
you
r an
swer
to
the
nea
rest
ten
th.
5
μg
c. A
fter
how
man
y da
ys w
ill
the
amou
nt
of v
acci
ne
be l
ess
than
1 μ
g?
afte
r 26
day
s
Wor
d Pr
oble
m P
ract
ice
Gro
wth
an
d D
ecay
Co
lleg
eS
ecto
rTu
itio
n a
nd
Fees
Ro
om
an
dB
oar
d
Fo
ur-
yea
r
Pu
blic
$5
94
1
$6
63
6
Fo
ur-
yea
r
Pri
vate
$2
1,2
35
$7,
79
1
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Answers (Lesson 7-6)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A18A15_A26_ALG1_A_CRM_C07_AN_660281.indd A18 12/24/10 9:30 AM12/24/10 9:30 AM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A19 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
40
Gle
ncoe
Alg
ebra
1
7-6
You
can
use
the
form
ula
for
com
poun
d in
tere
st A
= P
(1 +
r −
n ) n
t whe
n n
, the
num
ber
of t
imes
a
year
int
eres
t is
com
poun
ded,
is
know
n. A
spe
cial
typ
e of
com
poun
d in
tere
st c
alcu
lati
on
regu
larl
y us
ed i
n fi
nanc
e is
con
tin
uou
sly
com
pou
nd
ed i
nte
rest
, whe
re n
app
roac
hes
infi
nity
.
INV
ESTI
NG
Mr.
Riv
era
pla
ced
$50
00 i
n a
n i
nve
stm
ent
acco
un
t th
at
has
an
in
tere
st r
ate
of 9
.5%
per
yea
r.
Exer
cise
s
1. S
AV
ING
S M
r. H
arri
s sa
ves
$20,
000
in a
mon
ey-m
arke
t ac
cou
nt
at a
rat
e of
5.2
%.
a. D
eter
min
e th
e va
lue
of h
is i
nve
stm
ent
afte
r 10
yea
rs i
f in
tere
st i
sco
mpo
un
ded
quar
terl
y. $
33,5
28.0
1
b.
Det
erm
ine
the
valu
e of
his
in
vest
men
t af
ter
10 y
ears
if
inte
rest
is
com
pou
nde
d co
nti
nu
ousl
y. $
33,6
40.5
4
2. C
OLL
EGE
SAV
ING
S S
han
non
is
choo
sin
g be
twee
n t
wo
diff
eren
t sa
vin
gs a
ccou
nts
for
her
co
lleg
e fu
nd.
Th
e fi
rst
acco
un
t co
mpo
un
ds i
nte
rest
sem
ian
nu
ally
at
a ra
te o
f 11
.0%
. Th
e se
con
d ac
cou
nt
com
pou
nds
in
tere
st c
onti
nu
ousl
y at
a r
ate
of 1
0.8%
. If
Sh
ann
on p
lan
s to
ke
ep h
er m
oney
in
th
e ac
cou
nt
for
5 ye
ars,
wh
ich
acc
oun
t sh
ould
sh
e ch
oose
? E
xpla
in.
Sh
e sh
ou
ld c
ho
ose
th
e co
nti
nu
ou
s co
mp
ou
nd
ing
acc
ou
nt
at
10.8
%. A
fter
5 y
ears
, th
e va
lue
of
the
con
tin
uo
usl
y co
mp
ou
nd
ing
acc
ou
nt
will
be
1.71
6P, w
her
eas
the
qu
arte
rly
com
po
un
din
g a
cco
un
t w
ill o
nly
h
ave
a va
lue
of
1.70
8P.
Enri
chm
ent
Co
nti
nu
ou
sly
Co
mp
ou
nd
ing
In
tere
st
Ge
ne
ral fo
rmu
la: A
= P
ert
A =
cu
rre
nt
am
ou
nt
of
inve
stm
en
t
P =
in
itia
l a
mo
un
t o
f in
vestm
en
t
e =
na
tura
l lo
ga
rith
m,
a c
on
sta
nt
ap
pro
xim
ate
ly e
qu
al to
2.7
18
28
r =
an
nu
al ra
te o
f in
tere
st,
exp
resse
d a
s a
de
cim
al
t =
nu
mb
er
of
yea
rs t
he
mo
ney is inve
ste
d
Exam
ple
a. H
ow m
uch
mon
ey w
ill
be
in t
he
acco
un
t af
ter
5 ye
ars
if i
nte
rest
is
com
pou
nd
ed m
onth
ly?
A
= P
(1 +
r −
n ) n
t Co
mpound inte
rest
equation
= 5
000
(1 +
0.09
5 −
12
) 12
(5) P
= 5
000,
r =
0.0
95,
n =
12,
and t
= 5
= 5
000(
1.00
79)60
S
implif
y.
= 8
025.
05
Use a
calc
ula
tor.
T
her
e w
ill
be a
bou
t $8
025.
05 i
n t
he
acco
un
t if
in
tere
st i
s co
mpo
un
ded
mon
thly
.
b.
How
mu
ch m
oney
wil
l b
e in
th
e ac
cou
nt
afte
r 5
year
s if
in
tere
st i
s co
mp
oun
ded
con
tin
uou
sly?
A
= P
ert
Continuous inte
rest
equation
= 5
000(
2.71
828)
0.09
5(5)
P =
5000,
e =
2.7
1828,
r =
0.0
95,
and t
= 5
= 5
000(
2.71
828)
0.47
5 S
implif
y.
= 8
04
0.0
7
Use a
calc
ula
tor.
T
her
e w
ill
be a
bou
t $8
040.
07 i
n t
he
acco
un
t if
in
tere
st i
s co
mpo
un
ded
con
tin
uou
sly.
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-6
Cha
pte
r 7
41
Gle
ncoe
Alg
ebra
1
7-6
Spre
adsh
eet
Act
ivit
yC
om
po
un
d I
nte
rest
Exer
cise
s
Use
th
e sp
read
shee
t of
acc
oun
ts i
nvo
lvin
g co
mp
oun
d i
nte
rest
.
1. H
ow a
re t
he
dou
blin
g ti
mes
aff
ecte
d if
th
e ac
cou
nts
com
pou
nd
inte
rest
qu
arte
rly
inst
ead
of m
onth
ly?
Th
e 5%
an
d 8
% a
cco
un
ts d
ou
ble
in t
he
sam
e n
um
ber
of
year
s as
bef
ore
, bu
t th
e 10
% a
cco
un
t w
ill d
ou
ble
in 8
yea
rs.
2. H
ow l
ong
wil
l it
tak
e ea
ch a
ccou
nt
to r
each
$40
00 i
f th
e in
tere
st i
s co
mpo
un
ded
mon
thly
? qu
arte
rly?
mo
nth
ly:
5% in
28
yr, 8
% in
18
yr, 1
0% in
14
yr;
qu
arte
rly:
5%
in 2
8 yr
, 8%
in 1
8 yr
, 10%
in 1
5 yr
3. H
ow d
o th
e in
tere
st r
ate
and
the
nu
mbe
r of
tim
es t
he
inte
rest
is
com
pou
nde
d af
fect
th
e gr
owth
of
an i
nve
stm
ent?
Th
e ac
cou
nts
wit
h h
igh
er in
tere
st r
ate
and
inte
rest
co
mp
ou
nd
ed m
ore
oft
en g
row
mo
re q
uic
kly.
Ban
ks o
ften
use
spr
eads
hee
ts t
o ca
lcu
late
an
d st
ore
fin
anci
al d
ata.
On
e ap
plic
atio
n i
s to
ca
lcu
late
com
pou
nd
inte
rest
on
an
acc
oun
t.
U
se a
sp
read
shee
t to
fin
d t
he
tim
e it
wil
l ta
ke
an i
nve
stm
ent
of
$100
0 to
dou
ble
. Su
pp
ose
you
can
ch
oose
fro
m i
nve
stm
ents
th
at h
ave
ann
ual
in
tere
st r
ates
of
5%, 8
%, o
r 10
% c
omp
oun
ded
mon
thly
.T
he
com
pou
nd
inte
rest
equ
atio
n i
s A
= P
(1 +
r −
n ) n
t , wh
ere
P i
s th
e pr
inci
pal
or i
nit
ial
inve
stm
ent,
A i
s th
e fi
nal
am
oun
t of
th
e in
vest
men
t, r
is
the
ann
ual
in
tere
st r
ate,
n i
s th
e n
um
ber
of t
imes
in
tere
st i
s pa
id, o
r co
mpo
un
ded,
eac
h y
ear,
and
t is
th
e n
um
ber
of y
ears
. In
th
is c
ase,
P =
100
0 an
d n
= 1
2.
Ste
p 1
U
se C
olu
mn
A o
f th
e sp
read
shee
t fo
r th
e ye
ars.
Ste
p 2
C
olu
mn
s B
, C, a
nd
D c
onta
in t
he
form
ula
s fo
r th
e fi
nal
am
oun
ts o
f th
e in
vest
men
ts. F
orm
at t
he
cell
s in
th
ese
colu
mn
s as
cu
rren
cy s
o th
at t
he
amou
nts
are
sh
own
in
do
llar
s an
d ce
nts
. Eac
h f
orm
ula
w
ill
use
th
e va
lues
in
Col
um
n A
as
th
e va
lue
of t
. For
exa
mpl
e,
the
form
ula
th
at i
s in
cel
l C
3 is
=1
000*
(1 +
(0.0
8/12
))^(1
2 *
A3)
.S
tudy
th
e sp
read
shee
t fo
r th
e ti
mes
wh
en
each
in
vest
men
t ex
ceed
s $2
000.
At
5%, t
he
$100
0 w
ill
dou
ble
in 1
4 ye
ars,
at
8% i
t w
ill
dou
ble
in 9
yea
rs, a
nd
at 1
0% i
t w
ill
dou
ble
in 7
yea
rs.
A1 3 4 5 6 7 8 9 10 112
BC
D
12 13 14 15 16
Yea
rs$
1,0
51
.16
$1
,10
4.9
4
$1
,16
1.4
7
$1
,22
0.9
0
$1
,28
3.3
6
$1
,34
9.0
2
$1
,41
8.0
4
$1
,49
0.5
9
$1
,56
6.8
5
$1
,64
7.0
1
$1
,73
1.2
7
$1
,81
9.8
5
$1
,91
2.9
6
$2
,01
0.8
3
5%8%
10%
$1
,08
3.0
0
$1
,17
2.8
9
$1
,27
0.2
4
$1
,37
5.6
7
$1
,48
9.8
5
$1
,61
3.5
0
$1
,74
7.4
2
$1
,89
2.4
6
$2
,04
9.5
3
$2
,21
9.6
4
$2
,40
3.8
7
$2
,60
3.3
9
$2
,81
9.4
7
$3
,05
3.4
8
$1
,10
4.7
1
$1
,22
0.3
9
$1
,34
8.1
8
$1
,48
9.3
5
$1
,64
5.3
0
$1
,81
7.5
9
$2
,00
7.9
2
$2
,21
8.1
8
$2
,45
0.4
5
$2
,70
7.0
4
$2
,99
0.5
0
$3
,30
3.6
5
$3
,64
9.5
8
$4
,03
1.7
4
1 2 3 4 5 6 7 8 9
10
11
12
13
14
Sh
eet
1S
hee
t 2
Sh
eet
3
Exam
ple
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Answers (Lesson 7-6)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A19A15_A26_ALG1_A_CRM_C07_AN_660281.indd A19 12/20/10 7:11 PM12/20/10 7:11 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 7 A20 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
42
Gle
ncoe
Alg
ebra
1
7-7
Rec
og
niz
e G
eom
etri
c Se
qu
ence
s A
geo
met
ric
sequ
ence
is
a se
quen
ce i
n w
hic
h
each
ter
m a
fter
th
e fi
rst
is f
oun
d by
mu
ltip
lyin
g th
e pr
evio
us
term
by
a n
onze
ro c
onst
ant
r ca
lled
th
e co
mm
on r
atio
. Th
e co
mm
on r
atio
can
be
fou
nd
by d
ivid
ing
any
term
by
its
prev
iou
s te
rm.
Exer
cise
s
Det
erm
ine
wh
eth
er e
ach
seq
uen
ce i
s a
rith
met
ic, g
eom
etri
c, o
r n
eith
er. E
xpla
in.
1. 1
, 2, 4
, 8, .
. .
2. 9
, 14,
6, 1
1, .
. .
3.
2 −
3 ,
1 −
3 ,
1 −
6 ,
1 −
12 ,
. . .
4. –
2, 5
, 12,
19,
. . .
Fin
d t
he
nex
t th
ree
term
s in
eac
h g
eom
etri
c se
qu
ence
.
5. 6
48, –
216,
72,
. . .
6.
25,
–5,
1, .
. .
7.
1 −
16 ,
1 −
2 ,
4, .
. .
8. 7
2, 3
6, 1
8, .
. .
Stud
y G
uide
and
Inte
rven
tion
Geo
metr
ic S
eq
uen
ces a
s E
xp
on
en
tial
Fu
ncti
on
s
Exam
ple
1
Det
erm
ine
wh
eth
er t
he
seq
uen
ce i
s a
rith
met
ic, g
eom
etri
c, o
r n
eith
er: 2
1, 6
3, 1
89, 5
67, .
. .
Fin
d th
e ra
tios
of
the
con
secu
tive
ter
ms.
If
th
e ra
tios
are
con
stan
t, t
he
sequ
ence
is
geom
etri
c.21
63
18
9 56
7
63
−
21
=
18
9 −
63
=
567
−
189
= 3
Bec
ause
the
rat
ios
are
cons
tant
, the
seq
uenc
e is
geo
met
ric.
The
com
mon
rat
io is
3.
F
ind
th
e n
ext
thre
e te
rms
in t
his
geo
met
ric
seq
uen
ce:
-12
15, 4
05, -
135,
45,
. . .
Ste
p 1
F
ind
the
com
mon
rat
io.
–121
5 40
5 –1
35
45
40
5 −
-
1215
=
-
135
−
405
=
45
−
-13
5 =
-
1
−
3
Th
e va
lue
of r
is
- 1 −
3 .
Ste
p 2
M
ult
iply
eac
h t
erm
by
the
com
mon
ra
tio
to f
ind
the
nex
t th
ree
term
s.
45
–1
5
5
- 5
−
3
× (-
1 −
3 )
×
(-
1
−
3 )
× (-
1 −
3 )
Th
e n
ext
thre
e te
rms
of t
he
sequ
ence
ar
e –15
, 5, a
nd
- 5
−
3
.
Exam
ple
2
Geo
met
ric;
co
mm
on
rat
io is
2.
Nei
ther
; th
ere
is n
o c
om
mo
n
diff
eren
ce o
r ra
tio
.
Geo
met
ric;
co
mm
on
rat
io is
1 −
2 .A
rith
met
ic; c
om
mo
n d
iffer
ence
is 7
.
-24
, 8, -
2 2 −
3
32, 2
56, 2
048
- 1 −
5 , 1 −
25 ,
-
1 −
125
9, 4
1 −
2 , 2 1 −
4
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6:39
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-7
Cha
pte
r 7
43
Gle
ncoe
Alg
ebra
1
7-7
Geo
met
ric
Seq
uen
ces
and
Fu
nct
ion
s T
he
nth
ter
m a
n o
f a
geom
etri
c se
quen
ce
wit
h f
irst
ter
m a
1 an
d co
mm
on r
atio
r i
s gi
ven
by
the
foll
owin
g fo
rmu
la, w
her
e n
is
any
posi
tive
in
tege
r: a
n =
a1
· rn
– 1.
Exer
cise
s
1. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
–2,
10,
–50
, . .
. .
Fin
d th
e el
even
th t
erm
of
this
seq
uen
ce.
2. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
512
, 128
, 32,
. . .
. F
ind
the
sixt
h t
erm
of
this
seq
uen
ce.
3. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
4 −
9 ,
4, 3
6, .
. . .
Fin
d th
e ei
ghth
ter
m o
f th
is s
equ
ence
.
4. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
6, –
54, 4
86, .
. . .
F
ind
the
nin
th t
erm
of
this
seq
uen
ce.
5. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
100
, 80,
64,
. . .
. F
ind
the
seve
nth
ter
m o
f th
is s
equ
ence
.
6. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
2 −
5 ,
1 −
10 ,
1 −
40
, . .
. .
Fin
d th
e si
xth
ter
m o
f th
is s
equ
ence
.
7. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
3 −
8 ,
- 3 −
2 ,
6, .
. . .
Fin
d th
e te
nth
ter
m o
f th
is s
equ
ence
.
8. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
–3,
–21
, –14
7, .
. . .
Fin
d th
e fi
fth
ter
m o
f th
is s
equ
ence
.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Geo
metr
ic S
eq
uen
ces a
s E
xp
on
en
tial
Fu
ncti
on
s
Exam
ple
a.
Wri
te a
n e
qu
atio
n f
or
the
nth
ter
m o
f th
e ge
omet
ric
seq
uen
ce
5, 2
0, 8
0, 3
20, .
. .
Th
e fi
rst
term
of
the
sequ
ence
is
320.
So,
a 1
= 3
20. N
ow f
ind
the
com
mon
rat
io.
5
20
80
320
20
−
5 =
80
−
20
=
32
0 −
80
=
4
Th
e co
mm
on r
atio
is
4. S
o, r
= 4
.a n
= a
1 ·
rn –
1
Form
ula
for
nth t
erm
a n =
5 ·
4n
– 1
a 1 =
5 a
nd r
= 4
b.
Fin
d t
he
seve
nth
ter
m o
f th
is
seq
uen
ce.
Bec
ause
we
are
look
ing
for
the
seve
nth
ter
m,
n =
7.
a n =
a1
· rn
– 1
Form
ula
for
nth t
erm
a 7 = 5
· 4
7 – 1
n =
7
=
5 ·
46
Sim
plif
y.
=
5 ·
409
6 4
6 =
4096
=
20,
480
Multip
ly.
Th
e se
ven
th t
erm
of
the
sequ
ence
is
20,4
80.
an =
-
3 · 7n
- 1; -
7203
an =
3 −
8 · (-
4)n
- 1; -
98,3
04
an =
2 −
5 · (
1 −
4 ) n -
1 ;
1 −
2560
an =
10
0 · (
4 −
5 ) n -
1 ; 2
6 13
4 −
625
an =
6
· (-
9)n
- 1; 2
58,2
80,3
26
an =
4 −
9 · 9
n -
1; 2
,125
,764
an =
51
2 · ( 1
−
4 ) n -
1 ;
1 −
2
an =
-
2 · (-
5)n
- 1; -
19,5
31,2
50
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Answers (Lesson 7-7)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A20A15_A26_ALG1_A_CRM_C07_AN_660281.indd A20 12/20/10 7:11 PM12/20/10 7:11 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF 2nd
Chapter 7 A21 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
44
Gle
ncoe
Alg
ebra
1
7-7
Det
erm
ine
wh
eth
er e
ach
seq
uen
ce i
s a
rith
met
ic, g
eom
etri
c, o
r n
eith
er. E
xpla
in.
1. 7
, 13,
19,
25,
…
2. –
96, –
48, –
24, –
12, …
3. 1
08, 6
6, 1
41, 9
9, …
4.
3, 9
, 81,
656
1, …
5.
7 −
3 ,
14,
84,
504
, …
6. 3 −
8 ,
- 1 −
8 , -
5 −
8 ,
- 9 −
8 ,
…
Fin
d t
he
nex
t th
ree
term
s in
eac
h g
eom
etri
c se
qu
ence
.
7. 2
500,
500
, 100
, …
8. 2
, 6, 1
8, …
9. –
4, 2
4, –
144,
…
10.
4 −
5 ,
2 −
5 ,
1 −
5 ,
…
11. –
3, –
12, –
48, …
12
. 72,
12,
2, …
13. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
3, –
24,
192
, ….
Fin
d th
e n
inth
ter
m o
f th
is s
equ
ence
.
14. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
9 −
16
, 3 −
8 ,
1 −
4 ,
….
Fin
d th
e se
ven
th t
erm
of
this
seq
uen
ce.
15. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
100
0, 2
00, 4
0, …
. F
ind
the
fift
h t
erm
of
this
seq
uen
ce.
16. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
– 8
, – 2
, - 1 −
2 ,
….
Fin
d th
e ei
ghth
ter
m o
f th
is s
equ
ence
.
17. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
32,
48,
72,
….
Fin
d th
e si
xth
ter
m o
f th
is s
equ
ence
.
18. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
3
−
100 ,
3 −
10
, 3,
….
Fin
d th
e n
inth
ter
m o
f th
is s
equ
ence
.
Skill
s Pr
acti
ceG
eo
metr
ic S
eq
uen
ces a
s E
xp
on
en
tial
Fu
ncti
on
s
Ari
thm
etic
; co
mm
on
d
iffer
ence
is 6
.G
eom
etri
c; t
he
com
mo
n
rati
o is
1 −
2 .
Nei
ther
; th
ere
is n
o c
om
mo
n
diff
eren
ce o
r ra
tio
.N
eith
er; t
her
e is
no
co
mm
on
d
iffer
ence
or
rati
o.
Geo
met
ric;
co
mm
on
ra
tio
is 6
.A
rith
met
ic; c
om
mo
n
diff
eren
ce is
-
1 −
2 .
20, 4
, 4 −
5 54
, 162
, 486
864;
-51
84; 3
1,10
4
-19
2, -
768,
-30
72
1 −
10 ,
1 −
20 ,
1 −
40
1 −
3 , 1 −
18 ,
1
−
108
3(-
8) n
- 1 ;
50,
331,
648
3
−
100 ·
10
n -
1 ;
3,0
00,
00
0
9 −
16 ( 2
−
3 ) n -
1 ;
4 −
81
100
0 ( 1 −
5 ) n
- 1 ; 8
−
5
32 ( 3
−
2 ) n -
1
; 243
-8 (
1 −
4 ) n -
1 ; -
1
−
2048
041_
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10
9:22
AM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-7
Cha
pte
r 7
45
Gle
ncoe
Alg
ebra
1
7-7
Det
erm
ine
wh
eth
er e
ach
seq
uen
ce i
s a
rith
met
ic, g
eom
etri
c, o
r n
eith
er. E
xpla
in.
1. 1
, -5,
-11
, -17
, …
2. 3
, 3 −
2 ,
1, 3 −
4 ,
…
3. 1
08, 3
6, 1
2, 4
, …
4. -
2, 4
, -6,
8, …
Fin
d t
he
nex
t th
ree
term
s in
eac
h g
eom
etri
c se
qu
ence
.
5. 6
4, 1
6, 4
, …
6. 2
, -12
, 72,
…
7. 3
750,
750
, 150
, …
8. 4
, 28,
196
, …
9. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
896
, -44
8, 2
24, …
. F
ind
the
eigh
th t
erm
of
this
seq
uen
ce.
10. W
rite
an
equ
atio
n f
or t
he
nth
ter
m o
f th
e ge
omet
ric
sequ
ence
358
4, 8
96, 2
24, …
. F
ind
the
sixt
h t
erm
of
this
seq
uen
ce.
11. F
ind
the
sixt
h t
erm
of
a ge
omet
ric
sequ
ence
for
wh
ich
a2 =
288
an
d r
= 1
−
4
.
12. F
ind
the
eigh
th t
erm
of
a ge
omet
ric
sequ
ence
for
wh
ich
a3 =
35
and
r =
7.
13. P
ENN
IES
Th
omas
is
savi
ng
pen
nie
s in
a ja
r. T
he
firs
t da
y h
e sa
ves
3 pe
nn
ies,
th
e se
con
d da
y 12
pen
nie
s, t
he
thir
d da
y 48
pen
nie
s, a
nd
so o
n. H
ow m
any
pen
nie
s do
es
Th
omas
sav
e on
th
e ei
ghth
day
?
Prac
tice
Geo
metr
ic S
eq
uen
ces a
s E
xp
on
en
tial
Fu
ncti
on
s
Ari
thm
etic
; th
e co
mm
on
d
iffer
ence
is -
6.N
eith
er; t
her
e is
no
co
mm
on
d
iffer
ence
or
rati
o.
Geo
met
ric;
th
e co
mm
on
ra
tio
is 1 −
3 .N
eith
er; t
her
e is
no
co
mm
on
d
iffer
ence
or
rati
o.
1; 1 −
4 ; 1 −
16
-43
2; 2
592;
-15
,552
30; 6
; 6 −
5 13
72; 9
604;
67,
228
an =
896
(- 1 −
2 ) n -
1 ;
-7
an =
358
4 ( 1 −
4 ) n -
1 ;
3.5
1.12
5
588,
245
49,1
52
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Answers (Lesson 7-7)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A21A15_A26_ALG1_A_CRM_C07_AN_660281.indd A21 12/24/10 9:29 AM12/24/10 9:29 AM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 7 A22 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
46
Gle
ncoe
Alg
ebra
1
7-7
1. W
OR
LD P
OPU
LATI
ON
Th
e C
IA
esti
mat
es t
he
wor
ld p
opu
lati
on i
s gr
owin
g at
a r
ate
of 1
.167
% e
ach
yea
r. T
he
wor
ld p
opu
lati
on f
or 2
007
was
abo
ut
6.6
bill
ion
.
a. W
rite
an
equ
atio
n f
or t
he
wor
ld
popu
lati
on a
fter
n y
ears
. (H
int:
Th
e co
mm
on r
atio
is
not
0.0
1167
.)
b.
Wh
at w
ill
the
esti
mat
ed w
orld
po
pula
tion
be
in 2
017?
2. M
USE
UM
S T
he
tabl
e sh
ows
the
ann
ual
vi
sito
rs t
o a
mu
seu
m i
n m
illi
ons.
Wri
te
an e
quat
ion
for
th
e pr
ojec
ted
nu
mbe
r of
vi
sito
rs a
fter
n y
ears
.
3. B
AN
KIN
G A
rnol
d h
as a
ban
k ac
cou
nt
wit
h a
beg
inn
ing
bala
nce
of
$500
0. H
e sp
ends
on
e-fi
fth
of
the
bala
nce
eac
h
mon
th. H
ow m
uch
mon
ey w
ill
be i
n t
he
acco
un
t af
ter
6 m
onth
s?
4. P
OPU
LATI
ON
Th
e ta
ble
show
s th
e pr
ojec
ted
popu
lati
on o
f th
e U
nit
ed S
tate
s th
rou
gh 2
050.
Doe
s th
is t
able
sh
ow a
n
arit
hm
etic
seq
uen
ce, a
geo
met
ric
sequ
ence
or n
eith
er?
Exp
lain
.
Sour
ce: U
.S. C
ensu
s B
urea
u
5. S
AV
ING
S A
CC
OU
NTS
A b
ank
offe
rs a
sa
vin
gs a
ccou
nt
wit
h a
0.5
% r
etu
rn e
ach
m
onth
.
a. W
rite
an
equ
atio
n f
or t
he
bala
nce
of
a sa
vin
gs a
ccou
nt
afte
r n
mon
ths.
(H
int:
Th
e co
mm
on r
atio
is
not
0.0
05.)
b.
Giv
en a
n i
nit
ial
depo
sit
of $
500,
w
hat
wil
l th
e ac
cou
nt
bala
nce
be
afte
r 15
mon
ths?
Wor
d Pr
oble
m P
ract
ice
Geo
metr
ic S
eq
uen
ces a
s E
xp
on
en
tial
Fu
ncti
on
s
Year
Vis
itors
(mill
ion
s)
14
26
39
413
1
−
2
n?
Year
Pro
ject
edP
op
ula
tio
n
20
00
28
2,1
25
,00
0
2010
30
8,9
36
,00
0
20
20
33
5,8
05
,00
0
20
30
36
3,5
84
,00
0
20
40
39
1,9
46
,00
0
20
50
419
,85
4,0
00
an =
6,
600,
00
0,0
00
· 1.
0116
7 n
- 1
abo
ut
7.4
bill
ion
an =
4
· ( 3 −
2 ) n -
1
$131
0.72
Nei
ther
, th
ere
is n
o c
om
mo
n r
atio
or
diff
eren
ce.
an =
p
· 1.
005
n
$538
.84
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7 -7
Cha
pte
r 7
47
Gle
ncoe
Alg
ebra
1
7-7
Pay i
t Fo
rward
Th
e id
ea b
ehin
d “p
ay i
t fo
rwar
d” i
s th
at o
n t
he
firs
t da
y, o
ne
pers
on d
oes
a go
od d
eed
for
thre
e di
ffer
ent
peop
le. T
hen
, on
th
e se
con
d da
y, t
hos
e th
ree
peop
le w
ill
each
per
form
goo
d de
eds
for
3 m
ore
peop
le, s
o th
at o
n D
ay 2
, th
ere
are
3 ×
3 o
r 9
good
dee
ds b
ein
g do
ne.
C
onti
nu
e th
is p
roce
ss t
o fi
ll i
n t
he
char
t. A
tre
e di
agra
m w
ill
hel
p yo
u f
ill
in t
he
char
t.
1. G
raph
th
e da
ta y
ou f
oun
d in
th
e ch
art
as o
rder
ed p
airs
an
d co
nn
ect
wit
h a
sm
ooth
cu
rve.
2. W
hat
typ
e of
fu
nct
ion
is
you
r gr
aph
fro
m E
xerc
ise
1?
Wri
te a
n e
quat
ion
th
at c
an b
e u
sed
to d
eter
min
e th
e n
um
ber
of g
ood
deed
s on
an
y gi
ven
day
, x.
exp
on
enti
al;
y =
3x
3. H
ow m
any
good
dee
ds w
ill
be p
erfo
rmed
on
Day
21?
10
,460
,353
,203
Th
e fo
rmu
la T
= 3 n
+ 1 -
3
−
2 c
an b
e u
sed
to d
eter
min
e th
e to
tal
nu
mbe
r of
goo
d de
eds
that
hav
e be
en p
erfo
rmed
, wh
ere
n r
epre
sen
ts t
he
day.
For
exa
mpl
e, o
n D
ay 2
, th
ere
hav
e be
en
3 +
9 o
r 12
goo
d de
eds
perf
orm
ed. U
sin
g th
e fo
rmu
la, y
ou g
et,
3 2 +
1 -
3
−
2 o
r 3 3
- 3
−
2 +
27 -
3
−
2 o
r a
tota
l of
12
good
dee
ds p
erfo
rmed
.
4. U
se t
he
form
ula
to
dete
rmin
e th
e ap
prox
imat
e n
um
ber
of g
ood
deed
s th
at h
ave
been
pe
rfor
med
th
rou
gh D
ay 2
1.
15,6
90,5
29,8
00
5. L
ook
up
the
wor
ld p
opu
lati
on. H
ow d
oes
you
r n
um
ber
from
Exe
rcis
e 4
com
pare
to
the
wor
ld p
opu
lati
on?
T
he
wo
rld
po
pu
lati
on
is a
pp
roxi
mat
ely
6,56
0,52
6,04
6. T
he
nu
mb
er o
f g
oo
d d
eed
s p
erfo
rmed
is g
reat
er t
han
th
e en
tire
wo
rld
po
pu
lati
on
.
Per
son
1
Day
2D
ay 1
New
Per
son
2
New
Per
son
1
New
Per
son
3
y
xO240
210
180
120
150 90 60 30
43
27
86
51
Day
# o
f D
eed
s
01
13
29
3 27
481
524
3Enri
chm
ent
041_
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Answers (Lesson 7-7)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A22A15_A26_ALG1_A_CRM_C07_AN_660281.indd A22 12/20/10 7:11 PM12/20/10 7:11 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A23 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
48
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
R
ecu
rsiv
e F
orm
ula
s
7-8
Usi
ng
Rec
urs
ive
Form
ula
s A
rec
urs
ive
form
ula
all
ows
you
to
fin
d th
e n
th t
erm
of
a se
quen
ce b
y pe
rfor
min
g op
erat
ion
s on
on
e or
mor
e of
th
e te
rms
that
pre
cede
it.
F
ind
th
e fi
rst
five
ter
ms
of t
he
seq
uen
ce i
n w
hic
h a
1 =
5 a
nd
a
n =
-2 a
n -
1 +
14,
if
n ≥
2.
Th
e gi
ven
fir
st t
erm
is
a 1
= 5
. Use
th
is t
erm
an
d th
e re
curs
ive
form
ula
to
fin
d th
e n
ext
fou
r te
rms.
a
2 =
-2 a
2 -
1 +
14
n =
2
a 4
= -
2 a 4
- 1 +
14
n =
4
=
-2 a
1 +
14
Sim
plif
y.
= -
2 a 3
+ 1
4 S
implif
y.
=
-2(
5) +
14
or 4
a 1
= 5
=
-2(
6) +
14
or 2
a 3
= 6
a
3 =
-2 a
3 -
1 +
14
n =
3
a 5
= -
2 a 5
- 1 +
14
n =
5
=
-2 a
2 +
14
Sim
plif
y.
= -
2 a 4
+ 1
4 S
implif
y.
=
-2(
4) +
14
or 6
a 2
= 4
=
-2(
2) +
14
or 1
0 a 4
= 2
Th
e fi
rst
five
ter
ms
are
5, 4
, 6, 2
, an
d 10
.
Exe
rcis
esF
ind
th
e fi
rst
five
ter
ms
of e
ach
seq
uen
ce.
1. a
1 =
-4,
a n =
3 a
n -
1 , n
≥ 2
2.
a 1
= 5
, a n =
2a
n -
1 , n
≥ 2
-
4, -
12, -
36, -
108,
-32
4 5
, 10,
20,
40,
80
3. a
1 =
8, a
n =
a n
- 1 -
6, n
≥ 2
4.
a 1
= -
32, a
n =
a n
- 1 +
13,
n ≥
2
8
, 2, -
4, -
10, -
16
-32
, -19
, -6,
7, 2
0
5. a
1 =
6, a
n =
-3 a
n -
1 +
20,
n ≥
2
6. a
1 =
-9,
a n =
2 a
n -
1 +
11,
n ≥
2
6
, 2, 1
4, -
22, 8
6 -
9, -
7, -
3, 5
, 21
7. a
1 =
12,
a n =
2 a
n -
1 -
10,
n ≥
2
8. a
1 =
-1,
a n =
4 a
n -
1 +
3, n
≥ 2
1
2, 1
4, 1
8, 2
6, 4
2 -
1, -
1, -
1, -
1, -
1
9. a
1 =
64,
a n =
0.5
a n
- 1 +
8, n
≥ 2
10
. a 1
= 8
, a n =
1.5
a n
- 1 , n
≥ 2
6
4, 4
0, 2
8, 2
2, 1
9 8
, 12,
18,
27,
40.
5
11. a
1 =
400
, a n =
1 −
2 a
n -
1 , n
≥ 2
12
. a 1
= 1 −
4 ,
a n =
a n
- 1 +
3 −
4 ,
n ≥
2
4
00,
20
0, 1
00,
50,
25
1 −
4 , 1,
7 −
4 , 5 −
2 , 13
−
4
Exam
ple
041_
054_
ALG
1_A
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M_C
07_C
R_6
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1.in
dd
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-8
Cha
pte
r 7
49
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Recu
rsiv
e F
orm
ula
s
Wri
tin
g R
ecu
rsiv
e Fo
rmu
las
Com
plet
e th
e fo
llow
ing
step
s to
wri
te a
rec
urs
ive
form
ula
for
an
ari
thm
etic
or
geom
etri
c se
quen
ce.
Ste
p 1
De
term
ine
if
the
se
qu
en
ce
is a
rith
me
tic o
r g
eo
me
tric
by fi n
din
g a
co
mm
on
diff
ere
nce
or
a c
om
mo
n r
atio.
Ste
p 2
Wri
te a
re
cu
rsiv
e fo
rmu
la.
Ari
thm
etic
Seq
uen
ces
a n
= a
n -
1 +
d,
wh
ere
d is t
he
co
mm
on
diff
ere
nce
Geo
met
ric
Seq
uen
ces
a n =
r ·
an
- 1,
wh
ere
r is t
he
co
mm
on
ra
tio
Ste
p 3
Sta
te t
he
fi r
st
term
an
d t
he
do
ma
in fo
r n.
W
rite
a r
ecu
rsiv
e fo
rmu
la f
or 2
16, 3
6, 6
, 1, …
.
Ste
p 1
F
irst
su
btra
ct e
ach
ter
m f
rom
th
e te
rm t
hat
fol
low
s it
.21
6 -
36
= 1
80
36 −
6 =
30
6 -
1 =
5T
her
e is
no
com
mon
dif
fere
nce
. Ch
eck
for
a co
mm
on r
atio
by
divi
din
g ea
ch t
erm
by
the
term
th
at p
rece
des
it.
36
−
216 =
1 −
6
6 −
36 =
1 −
6
1 −
6 =
1 −
6
Th
ere
is a
com
mon
rat
io o
f 1 −
6 . T
he
sequ
ence
is
geom
etri
c.
Ste
p 2
U
se t
he
form
ula
for
a g
eom
etri
c se
quen
ce.
a n =
r ·
a n
- 1
Recurs
ive form
ula
for
geom
etr
ic s
equence
a n =
1 −
6 a
n -
1
r = 1
−
6
Ste
p 3
T
he
firs
t te
rm a
1 is
216
an
d n
≥ 2
.
A r
ecu
rsiv
e fo
rmu
la f
or t
he
sequ
ence
is
a 1
= 2
16, a
n =
1 −
6 a
n -
1 , n
≥ 2
.
Exer
cise
sW
rite
a r
ecu
rsiv
e fo
rmu
la f
or e
ach
seq
uen
ce.
1. 2
2, 1
6, 1
0, 4
, …
2. -
8, -
3, 2
, 7, …
a
1 =
22,
a n =
a n
- 1 -
6, n
≥ 2
a
1 =
-8,
a n =
a n
- 1 +
5, n
≥ 2
3. 5
, 15,
45,
135
, …
4. 2
43, 8
1, 2
7, 9
, …
a
1 =
5, a
n =
3 a
n -
1 , n
≥ 2
a
1 =
243
, a n =
1 −
3 a n
- 1 , n
≥ 2
5. −
3, 1
4, 3
1, 4
8, …
6.
8, -
20, 5
0, -
125,
…
a
1 =
-3,
a n =
a n
- 1 +
17,
n ≥
2
a 1
= 8
, a n =
-2.
5 a n
− 1 , n
≥ 2
7-8
Exam
ple
041_
054_
ALG
1_A
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M_C
07_C
R_6
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1.in
dd
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10
6:39
PM
Answers (Lesson 7-8)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A23A15_A26_ALG1_A_CRM_C07_AN_660281.indd A23 12/20/10 7:11 PM12/20/10 7:11 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 7 A24 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
50
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceR
ecu
rsiv
e F
orm
ula
s
7-8
Fin
d t
he
firs
t fi
ve t
erm
s of
eac
h s
equ
ence
.
1. a
1 =
-11
, a n =
a n
− 1 −
7, n
≥ 2
2.
a 1
= 1
4, a
n =
a n
− 1 +
6.5
, n ≥
2
-11
, -18
, -25
, -32
, -39
1
4, 2
0.5,
27,
33.
5, 4
0
3. a
1 =
-3,
a n =
3a
n −
1 +
10,
n ≥
2
4. a
1 =
187
.5, a
n =
−0.
8 a n
- 1 , n
≥ 2
-
3, 1
, 13,
49,
157
1
87.5
, -15
0, 1
20, -
96, 7
6.8
5. a
1 =
1 −
2 ,
a n =
3 −
2 a
n -
1 +
1 −
4 ,
n ≥
2
6. a
1 =
1 −
5 ,
a n =
5 −
2 a
n -
1 -
1 −
2 ,
n ≥
2
1 −
2 , 1,
7 −
4 , 23
−
8 , 73
−
16
1 −
5 , 0,
-
1 −
2 , -
7 −
4 , -
39
−
8
Wri
te a
rec
urs
ive
form
ula
for
eac
h s
equ
ence
.
7. 7
, 28,
112
, 448
, …
8. 7
3, 5
2, 3
1, 1
0, …
a
1 =
7, a
n =
4 a
n −
1 , n
≥ 2
a
1 =
73,
a n =
a n
- 1 -
21,
n ≥
2
9. 4
, 1,
1 −
4 ,
1 −
16 ,
…
10. -
37, -
15, 7
, 29,
…
a
1 =
4, a
n =
1 −
4 a n
− 1 , n
≥ 2
a
1 =
-37
, a n =
a n
- 1 +
22,
n ≥
2
11. 0
.25,
0.3
7, 0
.49,
0.6
1, …
12
. 64,
-80
, 100
, -12
5, 1
56.2
5, …
a
1 =
0.2
5, a
n =
a n
- 1 +
0.1
2, n
≥ 2
a
1 =
64,
a n =
-1.
25 a
n -
1 , n
≥ 2
For
eac
h r
ecu
rsiv
e fo
rmu
la, w
rite
an
exp
lici
t fo
rmu
la. F
or e
ach
exp
lici
t fo
rmu
la,
wri
te a
rec
urs
ive
form
ula
.
13. a
1 =
38,
a n =
a n
- 1 -
17,
n ≥
2
14. a
n =
5n
- 1
6
a n =
-17
n +
55
a 1
= -
11, a
n =
a n
- 1 +
5, n
≥ 2
15. a
n =
50(
0.75
) n -
1
16. a
1 =
16,
a n =
4 a
n −
1 , n
≥ 2
a
1 =
50,
a n =
0.7
5 a n
- 1 , n
≥ 2
a
n =
16(
4 ) n
- 1
041_
054_
ALG
1_A
_CR
M_C
07_C
R_6
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1.in
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-8
Cha
pte
r 7
51
Gle
ncoe
Alg
ebra
1
Prac
tice
Recu
rsiv
e F
orm
ula
s
Fin
d t
he
firs
t fi
ve t
erm
s of
eac
h s
equ
ence
.
1. a
1 =
25,
a n =
a n
- 1 -
12,
n ≥
2
2. a
1 =
-10
1, a
n =
a n
- 1 +
38,
n ≥
2
25,
13,
1, -
11, -
23
-10
1, -
63, -
25, 1
3, 5
1
3. a
1 =
3.3
, a n =
a n
- 1 +
2.7
, n ≥
2
4. a
1 =
7, a
n =
-3 a
n -
1 +
20,
n ≥
2
3.3
, 6, 8
.7, 1
1.4,
14.
1 7
, -1,
23,
-49
, 167
5. a
1 =
20,
a n =
1 −
5 a
n -
1 , n
≥ 2
6.
a 1
= 2 −
3 ,
a n =
1 −
3 a
n -
1 -
2 −
9 , n
≥ 2
2
0, 4
, 4 −
5 , 4 −
25 ,
4 −
125
2 −
3 , 0,
-
2 −
9 , -
8 −
27 ,
-
26
−
81
Wri
te a
rec
urs
ive
form
ula
for
eac
h s
equ
ence
.
7. 8
0, -
40, 2
0, -
10, …
8.
87,
52,
17,
-18
, …
a
1 =
80,
a n =
-0.
5 a n
- 1 , n
≥ 2
a
1 =
87,
a n =
a n
- 1 -
35,
n ≥
2
9.
1 −
3 ,
4 −
15 ,
16
−
75 ,
64
−
375 ,
…
10.
4 −
5 ,
3 −
10 ,
- 1 −
5 ,
- 7 −
10
, …
a
1 =
1 −
3 , a
n =
4 −
5 a n
- 1 , n
≥ 2
a
1 =
4 −
5 , a
n =
a n
- 1 -
1 −
2 , n
≥ 2
11. 2
.6, 5
.2, 7
.8, 1
0.4,
…
12. 1
00, 1
20, 1
44, 1
72.8
, …
a 1
= 2
.6, a
n =
a n
- 1 +
2.6
, n ≥
2
a 1
= 1
00,
a n =
1.2
a n
- 1 , n
≥ 2
13. P
IZZA
Th
e to
tal
cost
s fo
r or
deri
ng
one
to f
ive
chee
se
pizz
as f
rom
Lu
igi’s
Piz
za P
alac
e ar
e sh
own
.
a. W
rite
a r
ecu
rsiv
e fo
rmu
la f
or t
he
sequ
ence
. a 1
= 7
, a n =
a n
- 1 +
5.5
, n ≥
2
b.
Wri
te a
n e
xpli
cit
form
ula
for
th
e se
quen
ce.
an =
5.5
n +
1.5
7-8
Tota
l Nu
mb
er o
f P
izza
s O
rder
edC
ost
1 $
7.0
0
2$
12
.50
3$
18
.00
4$
23
.50
5$
29
.00
041_
054_
ALG
1_A
_CR
M_C
07_C
R_6
6028
1.in
dd
5112
/20/
10
6:39
PM
Answers (Lesson 7-8)
A15_A26_ALG1_A_CRM_C07_AN_660281.indd A24A15_A26_ALG1_A_CRM_C07_AN_660281.indd A24 12/20/10 7:11 PM12/20/10 7:11 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 7 A25 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 7
52
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
Recu
rsiv
e F
orm
ula
s
1. A
SSEM
BLY
An
ass
embl
y li
ne
can
cre
ate
175
wid
gets
in
on
e h
our,
350
wid
gets
in
tw
o h
ours
, 525
wid
gets
in
th
ree
hou
rs,
700
wid
gets
in
fou
r h
ours
, an
d so
on
.
a. F
ind
the
nex
t 5
term
s in
th
e se
quen
ce.
875,
105
0, 1
225,
140
0, 1
575
b.
Wri
te a
rec
urs
ive
form
ula
for
th
e se
quen
ce.
a 1
= 1
75, a
n=
a n
- 1
+ 1
75, n
≥ 2
c. W
rite
an
exp
lici
t fo
rmu
la f
or t
he
sequ
ence
. a
n=
175
n
2. P
APE
R A
pie
ce o
f pa
per
is f
olde
d se
vera
l ti
mes
. Th
e n
um
ber
of s
ecti
ons
into
wh
ich
th
e pi
ece
of p
aper
is
divi
ded
afte
r ea
ch
fold
is
show
n b
elow
.
Nu
mb
er o
f Fo
lds
Sec
tio
ns
12
24
38
416
53
2
a. F
ind
the
nex
t 5
term
s in
th
e se
quen
ce.
64, 1
28, 2
56, 5
12, 1
024
b.
Wri
te a
rec
urs
ive
form
ula
for
th
e se
quen
ce.
a 1
= 2
, a n =
2 a
n -
1 , n
≥ 2
c. W
rite
an
exp
lici
t fo
rmu
la f
or t
he
sequ
ence
. a
n =
2 n
3. C
LEA
NIN
G A
n e
quat
ion
for
th
e co
st
a n i
n d
olla
rs t
hat
a c
arpe
t cl
ean
ing
com
pan
y ch
arge
s fo
r cl
ean
ing
n r
oom
s is
a
n=
50
+ 2
5(n
- 1
). W
rite
a r
ecu
rsiv
e fo
rmu
la t
o re
pres
ent
the
cost
a n.
a 1
= 5
0, a
n=
a n
- 1
+ 2
5, n
≥ 2
4. S
AV
ING
S A
rec
urs
ive
form
ula
for
th
e ba
lan
ce o
f a
savi
ngs
acc
oun
t a
n i
n
doll
ars
at t
he
begi
nn
ing
of y
ear
n i
s a
1 =
500
, an =
1.0
5 a n
- 1 , n
≥ 2
. Wri
te a
n
expl
icit
for
mu
la t
o re
pres
ent
the
bala
nce
of
th
e sa
vin
gs a
ccou
nt
a n .
a n =
50
0(1.
0 5) n
- 1
5. S
NO
W A
sn
owm
an b
egin
s to
mel
t as
th
e te
mpe
ratu
re r
ises
. Th
e h
eigh
t of
th
e sn
owm
an i
n f
eet
afte
r ea
ch h
our
is
show
n.
Ho
ur
Hei
gh
t (f
t)
16
.0
25
.4
34
.86
44
.374
a. W
rite
a r
ecu
rsiv
e fo
rmu
la f
or t
he
sequ
ence
.
a 1
= 6
, a n =
0. 9
a n
- 1 , n
≥ 2
b.
Wri
te a
n e
xpli
cit
form
ula
for
th
e se
quen
ce.
a n =
6(0
.9 ) n
- 1
7-8
041_
054_
ALG
1_A
_CR
M_C
07_C
R_6
6028
1.in
dd
5212
/20/
10
6:39
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 7-8
Cha
pte
r 7
53
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Ari
thm
eti
c S
eri
es
7-8
Con
side
r a
situ
atio
n i
n w
hic
h a
n u
ncl
e gi
ves
his
nie
ce a
dol
lar
amou
nt
equ
al t
o h
er
age
each
yea
r on
her
bir
thda
y. A
n a
rith
met
ic s
equ
ence
th
at r
epre
sen
ts t
his
sit
uat
ion
is
1, 2
, 3, …
. H
ow m
uch
tot
al m
oney
wil
l th
e n
iece
hav
e re
ceiv
ed b
y h
er 3
0th
bir
thda
y?
Wh
en t
he
term
s of
an
ari
thm
etic
seq
uen
ce a
re a
dded
, an
ari
thm
etic
ser
ies
is f
orm
ed. T
he
solu
tion
of
the
prob
lem
abo
ve i
s th
e su
m o
f th
e ar
ith
met
ic s
erie
s 1
+ 2
+ 3
+ …
+ 3
0.
If w
e w
rite
th
e se
ries
tw
ice,
as
show
n b
elow
, an
d ad
d th
e te
rms
in e
ach
col
um
n, w
e ca
n
see
a pa
tter
n.
1
+
2 +
3
+
4 +
... +
27
+ 2
8 +
29
+ 3
0
30 +
29
+ 2
8 +
27
+ ..
. +
4 +
3
+
2 +
1
31
+ 3
1 +
31
+ 3
1 +
... +
31
+ 3
1 +
31
+ 3
1
Th
e su
m o
f ea
ch p
air
of t
erm
s is
31.
Mu
ltip
lyin
g 31
by
the
nu
mbe
r of
ter
ms
in t
he
bott
om
row
, 30,
giv
es u
s th
e su
m o
f th
e bo
ttom
row
, or
930.
Sin
ce t
he
seri
es w
as w
ritt
en t
wic
e, a
nd
resu
ltan
tly,
eac
h t
erm
in
th
e se
ries
was
acc
oun
ted
for
twic
e, w
e ca
n d
ivid
e 93
0 by
2 a
nd
fin
d th
at t
he
sum
of
the
seri
es 1
+ 2
+ 3
+ …
+ 3
0 is
465
.
1. W
rite
an
exp
ress
ion
to
repr
esen
t th
e su
m o
f th
e se
ries
abo
ve u
sin
g th
e fi
rst
term
1, t
he
last
ter
m 3
0, a
nd
the
nu
mbe
r of
ter
ms
in t
he
seri
es 3
0.
S
amp
le a
nsw
er:
30(1
+ 3
0)
−
2
2. W
rite
an
exp
ress
ion
to
repr
esen
t th
e su
m o
f an
ari
thm
etic
ser
ies
wit
h n
ter
ms,
fir
st
term
a 1 ,
and
last
ter
m a
n .
S
amp
le a
nsw
er:
n( a
1 +
a n )
−
2
Use
th
e ex
pre
ssio
n t
hat
you
fou
nd
in
Exe
rcis
e 2
to f
ind
th
e su
m o
f ea
ch
arit
hm
etic
ser
ies.
3. 1
+ 2
+ 3
+ …
+ 1
00
5050
4.
5 +
10
+ 1
5 +
… +
100
10
50
5. 1
+ 3
+ 5
+ …
+ 2
9 2
25
6. 2
+ 4
+ 6
+ …
+ 6
0 9
30
7. 6
+ 1
3 +
20
+ …
+ 1
25
1179
8.
8 +
12
+ 1
6 +
… +
84
920
041_
054_
ALG
1_A
_CR
M_C
07_C
R_6
6028
1.in
dd
5312
/20/
10
6:39
PM
Answers (Lesson 7-8)
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ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
PDF Pass
Chapter 7 A27 Glencoe Algebra 1
Chapter 7 Assessment Answer Key
An
swer
s
Quiz 2 (Lessons 7-3 and 7-4)Page 57
Quiz 4 (Lessons 7-7 and 7-8)Page 58
Quiz 1 (Lessons 7-1 and 7-2) Quiz 3 (Lessons 7-5 and 7-6) Mid-Chapter TestPage 57 Page 58 Page 59
B
3.08 × 10-5
1.4 × 107
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
3
8
3
2
2(7xy ) 1 − 2
9.0 × 106;9,000,000
-6 × 10-9;-0.000000006
2r 8
x20
-12t3n 7
-125x 12y 6
64c 8d 2
27y 4w 8
66 or 46,656
y 5
r2
− n9
C
a 1 = 3, a n = a n - 1 + 17, n ≥ 2
a 1 = 125, a n = -
1 −
5 a n - 1 ,
n ≥ 2
1.
2.
3.
4.
5.
-192, -768, -3072
C
Geometric; the common ratio is 1 −
2 .
1; D = all real numbers, R = {y|y > 0}
1.
y
xO
y = 13( )x
2.
y
xO
y = 4(2) -1 x
3.
4.
5.
A = 1500 (1 + 0.0485
−
4
) 4
˙
n
$2675.04
C
3; D = all real numbers, R = {y|y > -1}
1.
2.
3.
4.
5.
6.
7. B
G
D
F
A
F
B
8.
9.
10.
11.
12.
13.
5 m 6 y 3 r 5
−
7
2 −
5 x 9 y
6.72 × 104; 67,200
3.12 × 10-6; 0.00000312
4 −
3
-
2 −
3
Part II
Part I
A27_A32_ALG1_A_CRM_C07_AN_660281.indd A27A27_A32_ALG1_A_CRM_C07_AN_660281.indd A27 12/21/10 8:53 PM12/21/10 8:53 PM
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-Hill C
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panies, Inc.
PDF Pass
Chapter 7 A28 Glencoe Algebra 1
Chapter 7 Assessment Answer KeyVocabulary Test Form 1Page 60 Page 61 Page 62
Sample answer: A sequence in which each term after the fi rst is found by multiplying the previous term by a constant r, called the common ratio.
Sample answer: A function that can be described by an equation of the form y = a b x .
false; monomial
true
true
true
true
false; common ratio
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
true
false; order of magnitude
true
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
C
H
B
J
C
H
B
J
C
H
D
F 12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 39n + 1
B
F
C
J
C
H
A
G
A27_A32_ALG1_A_CRM_C07_AN_660281.indd A28A27_A32_ALG1_A_CRM_C07_AN_660281.indd A28 12/20/10 7:11 PM12/20/10 7:11 PM
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pyr
ight
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lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
PDF Pass
Chapter 7 A29 Glencoe Algebra 1
An
swer
s
Chapter 7 Assessment Answer KeyForm 2A Form 2BPage 63 Page 64 Page 65 Page 66
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
A
J
D
J
A
F
A
J
B
H
D
H 12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 7-2x - 2
D
F
B
G
D
J
A
J
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
B
H
B
G
A
J
B
J
B
G
C
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 37n - 1
H
D
H
D
J
C
G
D
G
A27_A32_ALG1_A_CRM_C07_AN_660281.indd A29A27_A32_ALG1_A_CRM_C07_AN_660281.indd A29 12/20/10 7:11 PM12/20/10 7:11 PM
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ivision o
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cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 7 A30 Glencoe Algebra 1
Chapter 7 Assessment Answer KeyForm 2CPage 67 Page 68
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. -
14 −
5
2
5 −
2
1.1
4 r 4 −
t 7
y −
x 5
8a 3n 6 + 4a18n 6
w 15y 12
-18t4n7
6.07 × 10-7
2.156 × 106; 2,156,000
4.5 × 108; 450,000,000
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
about $14,797.81
5, 2, −1
3, 10, 24
1 −
4
a 1 = 18, a n = a n - 1 + 11, n ≥ 2
a 1 = 2, a n = -6 a n - 1 , n ≥ 2
$1434.67
an = -3 · (-3)n - 1
1; D = all real numbers, R = {y|y > 0}
243
32
about 201 lb
3 √
��
22
3 4 √ �
x
y
xO
y = 7x
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ight
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McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
PDF Pass
Chapter 7 A31 Glencoe Algebra 1
An
swer
s
Chapter 7 Assessment Answer KeyForm 2DPage 69 Page 70
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
4.02 × 10-6
3r5t
d 7 −
2 a 5
10a 4b 8
w 9z 21
-6a 3b 8
1.3
1
-
17 −
12
4 −
3
4.1952 × 10-3;
0.0041952
2 × 103; 2000
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
a n = 4 · 2 n - 1
about $4595.27
about $5030.49
about 185 lb
10 3 √ �
x
1
a 1 = 27, a n = a n − 1 − 8, n ≥ 2
a 1 = 1296, a n =
1 −
6 a n − 1 , n ≥ 2
1, 2, 6
−4, 3, 10
4 √ ��
57
32
100
y
xO
y = 16( )x
1; D = all real numbers, R = {y|y > 0}
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-Hill C
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Chapter 7 A32 Glencoe Algebra 1
Chapter 7 Assessment Answer KeyForm 3Page 71 Page 72
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. 41
−
32
4 −
3
5 −
4
2
5.1
- 16 −
125a11b
mx 12 −
128
45x - 2
16
−
81 h 12
3.068 × 1011; 306,800,000,000
4.73 × 102
3.5 × 10-7;
0.00000035
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
a n = -7 · (-
1 −
4 )
n - 1
5 years
$112,206.07
0
about 577 lbs
a 1 = 50,
a n = a n − 1 − 47, n ≥ 2
a 1 = 1 −
8 , a n = 2 a n − 1 ,
n ≥ 2
3.5, −1, 1.25
2.25, 2.75, 3.25
8
8
√ ��
4yz
32 6 √ �
x
128
216
y
xOy = 4(2x - 1)
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An
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PDF Pass
Chapter 7 A33 Glencoe Algebra 1
An
swer
s
Chapter 7 Assessment Answer Key Page 73, Extended-Response Test Scoring Rubric
Score General Description Specifi c Criteria
4 Superior
A correct solution that
is supported by well-
developed, accurate
explanations
• Shows thorough understanding of the concepts of multiplying and dividing monomials, the degree of a polynomial, and adding, subtracting, and multiplying polynomials.
• Uses appropriate strategies to solve problems.
• Computations are correct.
• Written explanations are exemplary.
• Graphs are accurate and appropriate.
• Goes beyond requirements of some or all problems.
3 Satisfactory
A generally correct solution,
but may contain minor fl aws
in reasoning or computation
• Shows an understanding of the concepts of multiplying and dividing monomials, the degree of a polynomial, and adding, subtracting, and multiplying polynomials.
• Uses appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are effective.
• Graphs are mostly accurate and appropriate.
• Satisfi es all requirements of problems.
2 Nearly Satisfactory
A partially correct
interpretation and/or solution
to the problem
• Shows an understanding of most of the concepts of multiplying and dividing monomials, the degree of a polynomial, and adding, subtracting, and multiplying polynomials.
• May not use appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are satisfactory.
• Graphs are mostly accurate.
• Satisfi es the requirements of most of the problems.
1 Nearly Unsatisfactory
A correct solution with no
supporting evidence or
explanation
• Final computation is correct.
• No written explanations or work is shown to substantiate the
fi nal computation.
• Graphs may be accurate but lack detail or explanation.
• Satisfi es minimal requirements of some of the problems.
0 Unsatisfactory
An incorrect solution
indicating no mathematical
understanding of the concept
or task, or no solution is given
• Shows little or no understanding of most of the concepts of
multiplying and dividing monomials, the degree of a polynomial, and adding, subtracting, and multiplying polynomials.
• Does not use appropriate strategies to solve problems.
• Computations are incorrect.
• Written explanations are unsatisfactory.
• Graphs are inaccurate or inappropriate.
• Does not satisfy requirements of problems.
• No answer may be given.
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Chapter 7 A34 Glencoe Algebra 1
Chapter 7 Assessment Answer Key Page 73, Extended-Respo nse Test Sample Answers
1a. ( 4a3
−
2a-2 )
4 = (2a5)4
= 16a20
1b. ( 4a3
−
2a-2 )
4 =
(4a3) 4 −
(2a-2) 4 = 256a12
−
16a-8 = 16a20
1c. Sample answer: When simplifying monomials, the order of applying the Quotient of Powers property and Power of a Quotient property does not matter.
2a. Sample answer: In the geometric sequence 6, 3, 1.5, …, the value of r is 0.5 and the absolute value of a n + 1 will be closer to zero than the value of a n .
2b. Sample answer: In the recursive sequence, a 1 = 3, a 2 = 3, a n + 2 = a n + a n + 1 , the values of a 1 , a 2 , and a 3 are 3, 3, and 6, respectively. a 1 = a 2 , but a 2 ≠ a 3 .
3a. Sample answer: 5%; about 14.2 years
3b. Sample answer: 10%; about 6.6 years
3c. Sample answer: about 10.4 years; about $8320
4a. 5.97 × 1 0 24 kg
4b. 3.984 × 1 0 27 kg
4c. 47.66%
In addition to the scoring rubric found on page A33, the following sample answers
may be used as guidance in evaluating open-ended assessment items.
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Chapter 7 A35 Glencoe Algebra 1
An
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Chapter 7 Assessment Answer KeyStandardized Test PracticePage 74 Page 75
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Chapter 7 A36 Glencoe Algebra 1
Chapter 7 Assessment Answer KeyStandardized Test PracticePage 76
one solution; (2, 2)
35 −
6 + n = 2(n + 3)
3y2
−
x3
elimination (x); (1, –1)
Dallas Cowboys won
5 Super Bowls
Sample answer: c = Dallas Cowboys winsb = Denver Broncos wins; c + b = 7; c = 2.5b
a 1 = 39, a n =
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3 { }
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