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Algebraic Exponents & Exponential Functions Chapter Questions

1. How can you tell the difference between a linear and an exponential relationship?

2. Explain the difference between growth factors and growth rates.

3. Explain the difference between decay factors and decay rates.

NJ Center for Teaching and Learning www.njctl.org

Algebraic Exponents & Exponential Functions Chapter Problems

Exponential Growth Introduction

Classwork

1. The drama club wants to make confetti even faster. Now they decide to take one piece of paper and cut it into fourths. Then they stack the four pieces and cut them into fourths. They repeat this process creating smaller and smaller pieces of paper.

a. Create a table showing the number of cuts from 1 to 5 and the pieces of confetti.

b. How many pieces of confetti after 10 cuts?

c. How is this process different than when the paper was cut in halves and thirds?

2. For each expression below, identify the exponent and the base and write the answer.

a. 75

b. 113

c. 94

d. 105

e. 47

3. Write each expression in exponential form.

a. 4 x 4 x 4 x 4 =b. 7 x 7 x 7 x 7 x 7 x 7 =c. 3 x 3 =d. 9 x 9 x 9 x 9 x 9 =e. 12 x 12 x 12 x 12 =

4. Write each expression in standard form.

a. 83 = b. 56 =c. 27 =d. 93 =e. 144 =

5. Explain how the meanings of 24, 42 and 2 x 4 differ.

6. Find:

a. Five squaredb. Two to the fifth powerc. Nine cubed

7. Given 7x = 343, what is the value of x?



10. Given x6 = 4096, what is the value of x?




Write the product as a power.

13. 2 * 2 * 2 * 214. 8 * 8 * 8 * 8 * 8 * 8 * 815. m * m * m * m * m * m

Write using exponents.

16. 5 squared17. The fifth power of 718. P to the sixth

Evaluate each expression.

19. 24 =20. 33 =

21. 92 =22. 106 =

Homework

23. The drama club wants to make confetti even faster again. Now they decide to take one piece of paper and cut it into fifths. Then they stack the five pieces and cut them into fifths. They repeat this process creating smaller and smaller pieces of paper.

a. Create a table showing the number of cuts from 1 to 5 and the pieces of confetti.

b. How many pieces of confetti after 10 cuts?

c. How is this process different than when the paper was cut in halve, thirds, and fourths?

24. For each expression below, identify the exponent and the base and write the answer.

a. 35

b. 82

c. 104

d. 123

e. 67

25. Write each expression in exponential form.a. 5 x 5 x 5 =b. 2 x 2 x 2 x 2 x 2 x 2 =c. 10 x 10 x 10 x 10 =d. 8 x8 =e. 1 x 1 x 1 x 1 x 1 x 1 =

26. Write each expression in standard form.a. 124 = b. 47 =c. 105 =d. 36 =e. 810 =


27. Explain how the meanings of 35, 53 and 3 x 5 differ.

28. Find:

a. Eight to the fourth power

b. Four cubed

c. Twelve squared




32. Given x7 = 10,000,000 what is the value of x?



Write the product as a power.

35. 10 * 10 * 10 * 10 * 1036. 6 * 6 * 6 37. n * n38. y * y * y * y * y39. 94 * 94 * 94 * 94

Write using exponents.

40. q squared41. seven to the fourth42. three to the fifth

43. five cubed44. two to the sixth

Evaluate each expression

45. 53=46. 340 =47. 561=

48. 82 =49. 63 =

Exponential Growth v. Linear Growth

Classwork

Write whether the equation shows a linear growth or an exponential growth.

50. y=2x

51. y=23+x

52. y=3 x+7

53. y=3 x2


54. y=4 x3

Does the graph show an exponential growth or a linear growth?

55. __________________ 56. __________________ 57. __________________

Do the tables show an exponential growth or a linear growth?

58. __________________ 59. __________________ 60. __________________

Simplify.

61. m2 * m5 =62. c5 * c4 * c2 =63. y3 * y3 =64. 5z3 * z5 =65. 6p8 * 4p3=

66. b2 * b =67. d4 * d3 * d68. x3 * x * x5 * x4 =69. (3xy2)(8xy4) =70. p3 * q4 * q7 =

Homework

Write whether the equation shows a linear growth or an exponential growth.

71. y=2x+3

72. y=1.2 x2+4

73. y=1.2 x+32

74. y=4 x+1

75. y=2x3

Does the graph show an exponential growth or a linear growth?NJ Center for Teaching and Learning www.njctl.org

76. __________________ 77. __________________ 78. __________________

Do the tables show an exponential growth or a linear growth?

79. __________________ 80. __________________ 81. __________________

Simplify.

82. v7 * v7 =83. t * t8 * t10 =84. –n7 * -6n8 =85. -10z6 * 3z4 =86. x2 * x6 =

87. (-5u2v3)(4uv2) =88. (-3j3k)(-5j2k2) =89. 54n * -2n3 =90. a3 * c4 * c3 * a7 =91. w8 * w7 =

Exponential Relationships in Tables, Equations and Graphs

Classwork

92. In the table below:

a. What is the y intercept?

b. What is the growth factor?

c. What equation fits this data?

d. Graph the data on a coordinate plane.

x Y

0 1

1 3

2 9


3 27

4 81






x Y

0 1

1 5

2 25

3 125

4 625



b. Is there a growth factor? What type of relationship does the table show?


d. Graph the data on a coordinate plane. How does this graph differ from the first two examples?

x Y

0 1

1 5

2 9

3 13

4 17


95. You decide to start a garden at your house and plant Black-Eyed Susans. The next summer you notice that the flowers had reproduced significantly and you wrote the following equation n = 5(4t). In the equation n represents the number of flowers after t time in years.

a. How many flowers did you plant the first year?

b. What is the growth factor of the Black-Eyed Susans in the garden?

c. How many flowers will be in the garden after 4 years?

d. In how many years will there be over 5,000 plants in the garden?

96. The table below shows how a population of rabbits increases over several years.

a. Is the population linear or exponential or neither?

b. What is the starting population?

c. Write an equation to represent the data in the table.

Year Total rabbits

0 12

1 36

2 108

3 324

4 972


97. The table below shows how a population of whales increases over several years.




Year Total whales

0 50

1 55

2 60

3 65

4 70

98. For each table below decide if the relationship is linear, absolute value, exponential or none of them. If it represents one of them write the equation to represent the data.

Table A

X y

0 60

1 240

2 960

3 3840

4 15360

Table D

X y

5 6.5

6 9

7 11.5

8 14

9 16.5

Table B

x y

1 12

2 36

3 108

4 324

5 972

Table E

x Y

0 6

1 7

2 10

3 15

4 22

Table C

x Y

1 3

2 2

3 1

4 0

5 1

Table F


x Y

2 64

3 512

4 4096

5 32768

6 262144

Simplify.

99. a9 ÷ a4 =

100. x21 ÷ x5 =

101.107

103

102. 1321

137

103. 10a12÷5a3

104. 20x4

4 x2

Homework






X Y

0 1

1 4

2 16

3 64

4 256




c. What equation fits this data?NJ Center for Teaching and Learning www.njctl.org


X Y

0 1

1 7

2 79

3 343

4 2401



b. Is there a growth factor? What type of relationship does the table show?


d. Graph the data on a coordinate plane. How does this graph differ from the first two examples?

X Y

0 9

1 9.5

2 10

3 10.5

4 11

108. You decide to start a garden at your house and plant Black-Eyed Susans. The next summer you notice that the flowers had reproduced significantly and you wrote the following equation n = 8(4t). In the equation n represents the number of flowers after t time in years.

a. How many flowers did you plant the first year?

b. What is the growth factor of the Black-Eyed Susans in the garden?

c. How many flowers will be in the garden after 4 years?

d. In how many years will there be over 5,000 plants in the garden?NJ Center for Teaching and Learning www.njctl.org

109. The table below shows how a population of rabbits increases over several years.




110. The table below shows how a population of whales increases over several years.




Year Total whales

0 250

1 278

2 306

3 334NJ Center for Teaching and Learning www.njctl.org

Year Total rabbits

0 50

1 150

2 450

3 1350

4 4050

4 362

111. For each table below decide if the relationship is linear, absolute value, exponential or none of them. If it represents one of them write the equation to represent the data.

Table A

X y

0 12

1 9

2 6

3 3

4 0

Table D

X y

5 2

6 1

7 0

8 1

9 2

Table B

x y

1 55

2 275

3 1375

4 6875

5 34375

Table E

x y

0 10

1 30

2 90

3 270

4 810

Table C

x y

0 15

1 16

2 19

3 24

4 31

Table FNJ Center for Teaching and Learning www.njctl.org

x y

3 864

4 5184

5 31104

6 186624

7 1119744

Simplify

112. z14

z8

113. m20÷m18

114. s20

s15

115. 10473

1027

116. 434÷48

117.30x37

5x12

Growth Factors and Growth Rates

Classwork

118. What is the growth factor in each of the following exponential tables below?

Table A

X y

0 4

1 9.6

2 23.04

3 55.296

4 132.71

Table D

X Y

3 103.8

4 488.0

5 2293.5

6 10779.2

7 50662.3

Table B

x y

1 1.8

2 3.24NJ Center for Teaching and Learning www.njctl.org

3 5.83

4 10.50

5 18.90

Table E

x y

0 13

1 15.6

2 18.72

3 22.46

4 26.96

Table C

x Y

2 61.25

3 214.38

4 750.31

5 2626.09

6 9191.33

Table F


x Y

1 31.2

2 121.7

3 474.6

4 1850.8

5 7217.9

119. Fill in the table below with the missing growth factors and growth rates.

Growth factor

Growth rate

1.05 5%

25%

7%

1.42

2.5

1.20

50%

42%


1.43

120. If you invest $750 at a yearly interest rate of 7%:

a. What is the growth factor?b. How much money will you have after 6 years?





Evaluate.

123.

124. (-10)2=

125. (−2 )3=

126. (−2 )5=¿

127. (−3 )2=¿

128. (−3 )3=¿

129. (−1 )5=¿

130. (−10 )7=¿

131. (−4 )4=¿

132. (−7 )0=¿

133. (−8 )1=¿

Homework

134. What is the growth factor in each of the following exponential tables below?

Table A

X Y

0 3

1 5.1

2 8.67

3 14.74

4 25.06

Table B

X Y

3 31.25

4 78.13

5 195.31

6 488.28

7 1220.7

Table C

x y


1 4.2

2 17.6

3 74.1

4 311.2

5 1306.9

Table D

X y

0 6

1 20.4

2 69.36

3 235.82

4 801.8

Table E

x Y

2 5.293 12.17

4 27.98

5 64.36

6 148.04

Table F


x Y

1 13

2 16.9

3 21.97

4 28.56

5 37.13

135. Fill in the table below with the missing growth factors and growth rates.

Growth factor Growth rate

1.50 50%

1.45

1.07

4%

88%

1.23

1.40

28%

30%


a. What is the growth factor?

b. How much money will you have after 7 years?







Evaluate.

139.


140. (−6 )2=¿

141. (−6 )3=¿

142. (−3 )4=¿

143. (−3 )5=¿

144. (−5 )5=¿

145. (−10 )9=¿

146. (−7 )0=¿

147. (−10 )8=¿

148. (−6 )1=¿

149. (−4 )3=¿

Exponential Decay

Classwork

150. You have a bag of 500 pieces of candy and you eat a third of the pieces a day.

a. Create a table showing the candy remaining for days 0-8.

b. What is the y-intercept?

c. What is the decay factor?

d. What equation matches this situation?

151. You have another bag of candy with 700 pieces and you eat a fourth of the pieces a day.





152. Fill in the table below with the missing decay factors and decay rates.

Decay factor Decay rate

0.85 15%

0.50

0.25

30%

45%

0.90


0.05

90%

8%

Simplify.

153.

154. (x4)3=

155. (y2)5=

156. (c3)2=

157. (22)8=

158. (36)7=

159. (569)20=

160. (4318)3=

161. (w8)60=

162. (123)9=

163. (z5)6=

Homework

164. You have a bag of 850 pieces of candy and you eat half of the pieces a day.





165. You have another bag of candy with 1,000 pieces and you eat a fifth of the pieces a day.






166. Fill in the table below with the missing decay factors and decay rates.

Decay factor Decay rate

0.45 55%

0.03

0.65

28%

72%

0.32

0.48

53%

40%

Simplify.

167.

168. (163)9=

169. (126)3=

170. (x10)7=

171. (104)8=

172. (a6)7=

173. (t9)8=

174. (r7)7=

175. (33)2=

176. (q8)3=

177. (5412)3=

Rules for Exponents

Classwork

178. Complete each equation for the missing value:

a. (52)(55) = 5?

b. (127)(123) = 12?

c. (3-2)(35) = 3?

d. (49)(4-3) = 4?

e. (54)(5?) = 512

f. (107)(10?)(10-6) = 103


g. 34 ÷ 32 = 3?

h.

59

56= 5?

i.

95

98 = 9?

j. 124 ÷ 126 = 12?

k. 108 ÷ 10? = 103

l.

2?

23= 24

179. Simplify.

a. (4m5)2=

b. (-4z2)3=

c. (a2b3)4=

d. (-2x2y3)5

e. (2x3)4=

f. (-3h3)5=

g. (-4b3)3=

h. (5a3)5=

i. (3x2y4)4=

j. (-j7)2=

k. 3-4=

l. (-4)-3=

m. 7-1=

n. (-3)-2=

o. 11m-5=

p. 2a-3=

q. 7s-4=

r. 7s-4t2=

s. n-5v2=

t. 5-2p-1=

Homework

180. Complete each equation for the missing value:

a. (122)(127) = 12?

b. (25)(22) = 2?

c. (5-3)(55) = 5?

d. (158)(15-5) = 4?

e. (67)(6?) = 615

f. (11-6)(11?)(118) = 105

g. 77 ÷ 73 = 7?

h.

1110

116= 11?

i. 37 ÷ 39 = 3?

j.

26

210 = 2?

k.

136

13? = 132

l. 5? ÷ 56 = 53

181. Simplify.

a. (-3r)3=

b. (3y2)5=

c. (-2r5s2)6=

d. (xy2)5=NJ Center for Teaching and Learning www.njctl.org

e. (-a2b3)3=

f. (-2r2s)4=

g. (4uv5)3=

h. (c3)2=

i. (-d5)2=

j. (4x6y2)5=

k. 4-2=

l. (-x)-2=

m. (-5)-2=

n. 78-1=

o. 5x-4=

p. x-7=

q. 7ab-2=

r. r-4s2=

s. 3s-2=

t. x-5y7=

Unit Review

Multiple Choice– Choose the correct answer for each question.

1. Find three cubed.

a. 3 x 2 = 6

b. 3 x 3 = 9

c. 3 x 3 x 3 = 27

d. 3 x (3 x 3 x 3) = 81

2. Expressed in simplest form, (3x3)(3y2)2 (4x4) is equivalent to:

a. 36x12y4

b. 36x7y4

c. 108x12y4

d. 108x7y4

3. Given 6x = 216, find x.

a. 36

b. 3

c. 216

d. 4

4. In the equation y = 5(2x), what value does the 2 represent?

a. y-intercept

b. starting value

c. growth factor

d. growth rate

5. The expression 3–2 • 3-6 is equivalent to:

a. 312

b. 3-12

c. 3-8

d. 38

6. Given the equation y = 4(2x) if x = 4, what is the value of y?

a. 12

b. 32

c. 64

d. 8


7. Which of the following equations shows a linear relationship?

a. y=x2

b. y=2x+2

c. y=3 x2

d. y=4 x3+1

8. What is the y intercept of the following relationship?

x 1 2 3 4 5

y 9 27 81 243 729

a. 3

b. 15

c. 0

d. 5

9. What is the y intercept of the following relationship?

x 1 2 3 4

y 11 121 1331 14641

a. 0

b. 1

c. 10

d. 11

10. What is the growth factor in the following relationship?

x 2 3 4 5

y 11.56 39.304 133.6336 454.35424

a. 3

b. 3.2

c. 3.4

d. 5.78

11. If the growth rate is 10%, what is the growth factor?

a. 10

b. 1.1

c. 1.01

d. 100

12. If the growth factor is 1.6, what is the growth rate?

a. 6%

b. 60%

c. 16%

d. 160%

13. What is the equation for this table?

x 0 1 2 3 4

y 20 26 33.8 43.94 57.122

a. y = 1.3x

b. y = 1.3(20x)

c. y = 20(1.3x)

d. x = 1.3y


14. Identify the decay factor in the following table.

x 0 1 2 3 4

y 900 300 100 33.33 11.11

a. 900

b. 3

c. -3

d. 1/3

15. In a science e x p e r i m e n t , the a m o u n t o f b a c t e r i a d e c r e a s e d e a c h d a y . The table below shows the amount o f bac ter ia that remained at the start of work on successive days.

DayFractional Part of the bacteria remaining

112

214

318

Which fractional part of the rock will remain at noon on day 6?

a.1

128

b.1

64

c.1

14

d.112

Short Constructed Response – Write the correct answer for each question.

16. Explain how the meanings of 42, 24 and 4∙2 differ.

17. Create an exponential relationship and explain what the growth factor is for the relationship.

18. Suppose there is an initial rabbit population in the forest of 5,000 deer. The growth factor for the population is 1.2 per

year. How large will the deer population be in year 4?

19. What will y equal if x equals 6 in the equation y = 15(2.1x)?

20. What kind of growth does this table show?


X 0 1 2 3 4

y 5 10 20 40 80

Extended Constructed Response - Solve the problem, showing all work.

21. Given the following table:a. Explain why the relationship is exponential.b. Identify the:

i. Growth factorii. Growth rateiii. y intercept

c. Graph the relationship.d. Write the equation.

X 3 4 5 6

y 39.30 133.63 454.35 1544.80


Algebraic Exponents & Exponential Functions Chapter Problems Answer Key

Classwork

1

a.

1 4

2 16

3 64

4 256

5 1024

b. 1048576

c.

number of cuts

fourths halves thirds

1 4 2 3

2 16 4 9

3 64 8 27

4 256 16 81

5 1024 32 243

2

a. exponent 5, base 7, 16807

b. exponent 3, base 11, 1331

c. exponent 4, base 9, 6561

d. exponent 5, base 10, 100000

e. exponent 7, base 4, 16384

3.

a. 44

b. 76

c. 32

d. 95

e. 124

4.

a. 8●8●8

b. 5●5●5●5●5●5

c. 2●2●2●2●2●2●2

d. 9●9●9

e. 14●14●14●14

5. 24= 2●2●2●2 =16, 42 =4●4 =16, 2●4 =8

6.

a. 25

b. 32

c. 8

7. 3

8. 4

9. 6

10. 4

11. 10

12. 14

13. 24

14. 87

15. m6

16. 52

17. 75

18. P6

19. 16

20. 27

21. 81

22. 1000000


23.

a.

1 5

2 25

3 125

4 625

5 3125

b. 9765625

c.

Number of Cuts

Fifths Halves Thirds Fourths

1 5 2 3 4

2 25 4 9 16

3 125 8 27 64

4 625 16 81 256

5 3125 32 243 1024

24

a. exponent 5, base 3, 243

b. exponent 2, base 8, 64

c. exponent 4, base, 10000

d. exponent 3, base 12, 1728

e. exponent 7, base 6, 279936

25.

a. 53

b. 26

c. 104

d. 82

e. 16

26.

a. 12●12●12●12

b. 4●4●4●4●4●4●4

c. 10●10●10●10●10

d. 3●3●3●3●3●3

e. 8●8●8●8●8●8●8●8●8●8

27. 35 = 3●3●3●3●3 = 243, 53 = 5●5●5 = 125, 3●5 = 15

28.

a. 4096

b. 64

c. 144

29. 4

30. 2

31. 8

32. 10

33. 7

34. 3

35. 105

36. 63

37. n2

38. y5

39. 944

40. q2

41. 74

42. 35

43. 53

44. 26

45. 125

46. 1

47. 56

48. 64

49. 216

50. linear

51. linear

52. linear


53. exponential

54. exponential

55. linear

56. exponential

57. exponential

58. linear

59. exponential

60. linear

61. m7

62. 2c10

63. y6

64. 5z8

65. 24p11

66. b3

67. d8

68. x13

69. 24x2y6

70. p3q11

71. linear

72. exponential

73. linear

74. linear

75. exponential

76. exponential

77. linear

78. exponential

79. linear

80. exponential

81. exponential

82. v14

83. t19

84. 6n15

85. -30z10

86. x8

87. -20u3v5

88. 15j5k3

89. -108n4

90. a10c7

91. w15

92.

a. 1

b. 3

c. y = 3(1x)

d.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

20406080

100120140160

93.

a. 1

b. 5

c. y = 5(1x)

d.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

20406080

100120140160


94.

a. 1

b. no, linear

c. y = 4x + 1

d.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

20406080

100120140160

95.

a. 5

b. 4

c. 1280

d. 5 years

96.

a. exponential

b. 12

c. 12(3x)

97.

a. linear

b. 50

c. y = 5x + 50

98.

A. exponential, 60(4x)

B. exponential, 12(3x)

C. absolute value, │x-4│

D. linear, y = 2.5x-6

E. neither

F. exponential, 64(8x)

99. a5

100. x16

101. 104

102. 1314

103. 2a9

104. 5x2

105.

a. 1

b. 4

c. 4(1x)

d.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

20406080

100120140160

106.

a. 1

b. 7

c. 7(1x)

d.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

20406080

100120140160

107.

a. 9


b. none, linear

c. y = 28x+250

d.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

20406080

100120140160

108.

a. 32

b. 8

c. 2048

d. 5

109.

a. exponential

b. 50

c. 50(3x)

110.

a. linear

b. 250

c. y=28x+250

111.

A-linear, y=-3x+12

B-exponential, 55(5x)

C-neither

D-absolute value, │x-7│

E-exponential, 10(3x)

F-exponential, 864(6x)

112. z6

113. m2

114. s5

115. 10446

116. 426

117. 6x25

118.

A-2.4

B-1.8

C-3.5

D-4.7

E-1.2

F-3.9

119.

1.25, 1.07, 42%, 150%, 20%, 1.5, 1.42, 43%

120.

a. 1.07

b. 1125.57

121.

a. 1.03

b. 67.20

122.

a. 1.05

b. 1550.02

123. 100

124. -8

125. -32

126. 9

127. -27

128. -1

129. -10000000

130. 256

131. 1

132. -8


133.

A- 1.7

B- 2.5

C- 4.2

D- 3.4

E- 2.3

F- 1.3

134.

45%, 7%, 1.04, 1.88, 23%, 40%, 1.28, 1.3

135.

a. 1.04

b. 1184.34

136.

a. 1.07

b. 2621.59

137.

a. 1.05

b. 822.59

138. 36

139. -216

140. 81

141. -243

142. -3125

143. -1000000000

144. 1

145. 100000000

146. -6

147. -64

148.

0 500

1 333

2 222

3 148

4 99

5 66

6 44

7 29

8 19

b. 500

c. .66

d. 500(2/3)x

149.

a.

0 700

1 525

2 394

3 296

4 222

5 167

6 125

7 94

8 71

b. 700

c. .75

d. 700(3/4)x

150.

50%, 75%, .70, .55, 10%, 95%, .1, .92

151. x12


152. y10

153. c6

154. 216

155. 342

156. 56180

157. 4854

158. w480

159. 1227

160. z30

161.

0 850

1 425

2 213

3 107

4 54

5 27

6 14

7 7

8 4

b. 850

c. .5

d. 850(1/2)x

162.

0 1000

1 800

2 640

3 512

4 410

5 328

6 262

7 210

8 168

b. 1000

c. .8

d. 1000(4/5)x

163.

97%, 35%, .72, .28, 68%, 52%, .47, .60

164. 1627

165. 1218

166. x70

167. 1032

168. a42

169. t72

170. r49

171. 36

172. q24

173. 5436

174.

a. 57

b. 1210

c. 33

d. 46

e. 58


f. 102

g. 32

h. 53

i. 9-3

j. 12-2

k. 105

l. 27

175.

a. 4m10

b. -4z6

c. a8b12

d. -25x10y15

e. 24x12

f. -35h15

g. -43b9

h. 55a15

i. 34x8y16

j. –j14

k. 1/34

l. 1/(-4)3

m. 1/7

n. 1/(-3)2

o. 11/m5

p. 2/a3

q. 7/s4

r. 7t2/s4

s. v2/n5

t. 1/52p

176.

a. 1214

b. 210

c. 5-15

d. 15-40

e. 68

f. 113

g. 74

h. 114

i. 3-2

j. 2-4

k. 134

l. 59

177.

a. -33r3

b. 35y10

c. -26r30s12

d. x5y10

e. –a6b9

f. -24r8s4

g. 43u3v15

h. c6

i. –d10

j. 45x30y10

k. 1/42

l. 1/(-x)2

m. 1/(-5)2

n. 1/78

o. 5/x4

p. 1/x7

q. 7a/b2

r. s2/r4

s. 3/s2

t. y7/x5


Unit Review

1. C

2. B

3. B

4. C

5. C

6. C

7. B

8. A

9. B

10. C

11. B

12. B

13. C

14. D

15. B

16. 4●4=16, 2●2●2●2=16, 4●2=8

17. There is a petri dish full of bacteria. Every day the bacteria quadruple. In this problem the growth factor is 4 because the previous population is multiplied by four every day.

18.

0 1 2 3 4

5000 6000 7200 8640 10368

19. y=1286.49

20. exponential

21.

a. The relationship is exponential because the previous number is multiplied by 3.4 to receive the next number

b.

i. 3.4

ii. 1.034

iii. 1

c.

0 1 2 3 4 5 6 70

200400600800

10001200140016001800

d. 3.4x


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