Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Algebra II Quiz: Lessons 7.1 through 7.4 Review
Graph:
1. f x( ) = 4x
Name: ________________________ ID: A
2
____ 2. Graph the function: f x( ) = 3x
Name: ________________________ ID: A
3
a.
b.
Name: ________________________ ID: A
4
c.
d.
____ 3. Find the y-intercept of the equation. y = − 3 ⋅ 7x
a. 4 b. –21 c. –3 d. 7
4. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound
annual rate, r, is given by A = P(1 + r)n. If a person invests $250 in an account that pays 10% interest
compounded annually, find the balance after 15 years.
Name: ________________________ ID: A
5
____ 5. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound
annual rate, r, is given by A =P 1+ r( )n. If a person invests $310 in an account that pays 8% interest
compounded annually, find the balance after 5 years.
a. $455 b. $2790 c. $13,950 d. $443
6. The projected worth (in millions of dollars) of a large company is modeled by the equation y = 256 1.04( )x.
The variable x represents the number of years since 1997. What is the projected annual percent of growth,
and what should the company be worth be in 2007?
____ 7. The projected worth (in millions of dollars) of a large company is modeled by the equation y = 241 1.04( )x.
The variable x represents the number of years since 1997. What is the projected annual percent of growth,
and what should the company be worth in 2001?
a. 14%; $293.21 million c. 14%; $250.64 million
b. 4%; $271.09 million d. 4%; $281.94 million
8. Find the value of $1000 deposited for 8 years in an account paying 8% annual interest compounded semiannually.
9. How much money must be deposited now in an account paying 7% annual interest, compounded yearly, to have a balance of $1000 after 6 years?
____ 10. Sara bought 6 fish. Every month the number of fish she has doubles. After m months she will have F fish,
where F = 6 ⋅2m. How many fish will Sara have after 2 months if she keeps all of them and the fish stay
healthy?
a. 20 b. 10 c. 144 d. 24
____ 11. If there are initially 4000 bacteria in a culture, and the number of bacteria double each hour, the number of
bacteria after t hours can be found using the formula N = 4000 2tÊËÁÁÁ
ˆ¯˜̃̃ . How many bacteria will be present after
9 hours?
a. 2,048,000 b. 4,096,000 c. 1,024,000 d. 72,000
Name: ________________________ ID: A
6
____ 12. Graph the function: f x( ) =1
4
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃˜̃˜̃
x
Name: ________________________ ID: A
7
a.
b.
Name: ________________________ ID: A
8
c.
d.
13. Describe y=2.9x as an example of exponential growth or exponential decay.
Name: ________________________ ID: A
9
Graph:
____ 14. f(x) = 21
4
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃˜̃˜̃
x
a. c.
b. d.
Writing:
15. How does changing the value of b affect the graph of an exponential equation of the form y = abx?
Simplify:
____ 16. 7e
19
35e6
a. 5e25
c. 5e13
b.1
5e
13d.
1
5e
25
Simplify the expression.
17. ex
⋅ 6e3x − 1
Name: ________________________ ID: A
10
____ 18. Graph f x( ) = − 3 + ex.
a. c.
b. d.
19. Is f x( ) = 13.7e−0.04t
an example of exponential growth or decay?
20. Sketch the graph of the function. f x( ) =1
3e
x− 2
____ 21. If $2500 is invested at a rate of 11% compounded continuously, find the balance in the account after 4 years.
Use the formula A =Pert
.a. $3795.18 b. $3881.77 c. $4333.13 d. $18472.64
____ 22. The formula A = 2000ert
can be used to find the dollar value of an investment of $2000 after t years when the
interest is compounded continuously at a rate of r percent. Find the value of the investment after 6 years if
the interest rate is 7%. Find the value of the investment after 12 years if the interest rate is 8%.
a. $3043.92; $2920.47 c. $3043.92; $5223.39
b. $4901.85; $5223.39 d. $4901.85; $2920.47
True or False:
23. The formula for interest compounded continuously is A = Pet.
24. The formula for interest compounded continuously is A = Pert.
Name: ________________________ ID: A
11
Evaluate:
____ 25. log3729
a.1
6b. 18 c. 6 d.
1
18
____ 26. Graph the function y = 1.2x and its reflection over the line y = x. Is the reflection the graph of a function?
a.
No
c.
No
b.
Yes
d.
Yes
Name: ________________________ ID: A
12
Graph:
____ 27. y = log3 x
a. c.
b. d.
____ 28. Use the formula R = log10 I , where R is the measurement of the Richter scale and I is the intensity, to find the
Richter scale measurement of an earthquake with intensity 53,000,000.
a. 7.7243 b. 1.77858 c. 0.77243 d. 17.7858
29. Evaluate ln e−4
.
Graph the function. State the domain and range.
30. y = ln x + 2( )
ID: A
1
Algebra II Quiz: Lessons 7.1 through 7.4 Review
Answer Section
1. ANS:
PTS: 1 DIF: Level B REF: MAL21000 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: function | graph | exponentBLM: Knowledge NOT: 978-0-618-65615-8
2. ANS: B PTS: 1 DIF: Level B REF: MAL21002
TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: function | graph | exponentialBLM: Knowledge NOT: 978-0-618-65615-8
3. ANS: C PTS: 1 DIF: Level B REF: MAL21004
TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: exponential | equationBLM: Knowledge NOT: 978-0-618-65615-8
4. ANS:
$1044
PTS: 1 DIF: Level B REF: MAL21006 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth FunctionsKEY: word | log | compound interest BLM: Application NOT: 978-0-618-65615-8
5. ANS: A PTS: 1 DIF: Level B REF: MAL21007
STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth FunctionsKEY: word | log | compound interest BLM: Application NOT: 978-0-618-65615-8
6. ANS:
4%; $378.94 million
PTS: 1 DIF: Level B REF: MAL21008 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word | exponential growthBLM: Application NOT: 978-0-618-65615-8
7. ANS: D PTS: 1 DIF: Level B REF: MAL21009TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word | exponential | growthBLM: Application NOT: 978-0-618-65615-8
ID: A
2
8. ANS:
$1872.98
PTS: 1 DIF: Level A REF: MAL21014 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth FunctionsKEY: compound interest BLM: Application NOT: 978-0-618-65615-8
9. ANS:
$666.34
PTS: 1 DIF: Level B REF: MAL21017 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth FunctionsKEY: compound interest BLM: Application NOT: 978-0-618-65615-8
10. ANS: D PTS: 1 DIF: Level B REF: MAL21020TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: law of exponents | wordBLM: Application NOT: 978-0-618-65615-8
11. ANS: A PTS: 1 DIF: Level B REF: MAL21022TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word | exponential growthBLM: Application NOT: 978-0-618-65615-8
12. ANS: C PTS: 1 DIF: Level B REF: MAL21028TOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph | functionBLM: Knowledge NOT: 978-0-618-65615-8
13. ANS: exponential growth
PTS: 1 DIF: Level B REF: MAL21029 NAT: NCTM 9-12.ALG.1.cSTA: MI.MIGLC.MTH.06.9-12.A2.5.2 TOP: Lesson 7.2 Graph Exponential Decay FunctionsKEY: exponential growth | exponential decay BLM: ComprehensionNOT: 978-0-618-65615-8
14. ANS: D PTS: 1 DIF: Level B REF: MAL21031TOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph | exponential functionBLM: Knowledge NOT: 978-0-618-65615-8
15. ANS: Sample answer: For b > 0, as the value of b increases, the curve slopes upward faster; that is, the value of y increases at a faster rate. For 0 < b < 1, as the value of b increases, the curve slopes downward slower; that is, the value of y decreases at a slower rate.
PTS: 1 DIF: Level B REF: MAL21032 NAT: NCTM 9-12.ALG.1.cTOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph | exponentialBLM: Analysis NOT: 978-0-618-65615-8
16. ANS: B PTS: 1 DIF: Level B REF: MAL21041TOP: Lesson 7.3 Use Functions Involving e KEY: exponent | exponential | rules | simplify BLM: ComprehensionNOT: 978-0-618-65615-8
ID: A
3
17. ANS:
6e4x − 1
PTS: 1 DIF: Level B REF: MAL21042 TOP: Lesson 7.3 Use Functions Involving e KEY: exponent | multiply | eBLM: Comprehension NOT: 978-0-618-65615-8
18. ANS: D PTS: 1 DIF: Level B REF: MAL21049
TOP: Lesson 7.3 Use Functions Involving e KEY: function | graph | exponentialBLM: Knowledge NOT: 978-0-618-65615-8
19. ANS:
Decay
PTS: 1 DIF: Level A REF: MAL21052 STA: MI.MIGLC.MTH.06.9-12.A2.5.2TOP: Lesson 7.3 Use Functions Involving e KEY: function | exponential growth | exponential decay BLM: KnowledgeNOT: 978-0-618-65615-8
20. ANS:
PTS: 1 DIF: Level B REF: MAL21053 TOP: Lesson 7.3 Use Functions Involving e KEY: graph | exponential function | eBLM: Comprehension NOT: 978-0-618-65615-8
21. ANS: B PTS: 1 DIF: Level B REF: MAL21058
STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.3 Use Functions Involving eKEY: word | interest | compound | continuous BLM: ApplicationNOT: 978-0-618-65615-8
22. ANS: C PTS: 1 DIF: Level B REF: MAL21060STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.3 Use Functions Involving eKEY: interest | continuous | compounded continuously BLM: ApplicationNOT: 978-0-618-65615-8
ID: A
4
23. ANS:
False
PTS: 1 DIF: Level B REF: MAL21062 TOP: Lesson 7.3 Use Functions Involving e KEY: word | interest | e | compounded continuously BLM: ComprehensionNOT: 978-0-618-65615-8
24. ANS:
True
PTS: 1 DIF: Level B REF: MAL21063 TOP: Lesson 7.3 Use Functions Involving e KEY: e | compounded continuously | word | interest BLM: ComprehensionNOT: 978-0-618-65615-8
25. ANS: C PTS: 1 DIF: Level A REF: MAL21066TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: log | evaluate | exponential BLM: Knowledge NOT: 978-0-618-65615-8
26. ANS: B PTS: 1 DIF: Level B REF: MAL21076NAT: NCTM 9-12.GEO.3.a TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: graph | exponential | inverse | function BLM: ComprehensionNOT: 978-0-618-65615-8
27. ANS: C PTS: 1 DIF: Level B REF: MAL21081NAT: NCTM 9-12.ALG.1.c TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: log | graph BLM: Comprehension NOT: 978-0-618-65615-8
28. ANS: A PTS: 1 DIF: Level B REF: MAL21110STA: MI.MIGLC.MTH.06.9-12.A1.2.7 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: logarithms | word BLM: Application NOT: 978-0-618-65615-8
29. ANS: -4
PTS: 1 DIF: Level B REF: MAL21073 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: logarithm | e BLM: Knowledge NOT: 978-0-618-65615-8
ID: A
5
30. ANS:
Domain: x > −2; Range: all real numbers
PTS: 1 DIF: Level B REF: MAL21089 NAT: NCTM 9-12.ALG.1.cSTA: MI.MIGLC.MTH.06.9-12.A2.5.2 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: log | graph BLM: Comprehension NOT: 978-0-618-65615-8
Top Related