Deck 4: Exponential and Logarithmic Functions

Question 1

Approximate the number using a calculator. Round your answer to three decimal places.
The rabbit population in a forest area grows at the rate of $9 \%$ monthly. If there are 160 rabbits in July, find how many rabbits (rounded to the nearest whole number) should be expected by next July. Use $y = 160 ( 2.7 ) ^ { 0.09 t }$

A) 468
B) 467
C) 481
D) 455

Answer 1

A

Question 2

Graph the function by making a table of coordinates.
$f(x)=\left(\frac{1}{4}\right)^{x}$

A)

B)

C)

D)

Answer 2

A

Question 3

The graph of an exponential function is given. Select the function for the graph from the functions listed.

A) $f ( x ) = 3 ^ { x } - 2$
B) $f ( x ) = 3 ^ { x }$
C) $f ( x ) = 3 ^ { x - 2 }$
D) $f ( x ) = 3 ^ { x } + 2$

Answer 3

A

Question 4

Approximate the number using a calculator. Round your answer to three decimal places.
$4 ^ { - 2.9 }$

A) $0.018$
B) $- 11.600$
C) $70.728$
D) $0.318$

Question 5

Graph the function by making a table of coordinates.
$$f ( x ) = 0.7 ^ { x }$$

A)

B)

C)

D)

Question 6

Graph the function by making a table of coordinates.
$f(x)=5^{x}$

A)

B)

C)

D)

Question 7

Graph the function
Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x - 4 }$ .

A)

B)

C)

D)

Question 8

The graph of an exponential function is given. Select the function for the graph from the functions listed.

A) $f ( x ) = - 5 ^ { - x }$
B) $f ( x ) = 5 ^ { x }$
C) $f ( x ) = - 5 ^ { x }$
D) $f ( x ) = 5 ^ { - x }$ .

Question 9

The graph of an exponential function is given. Select the function for the graph from the functions listed.

A) $f ( x ) = - 3 ^ { x }$
B) $f ( x ) = 3 ^ { x }$
C) $f ( x ) = 3 ^ { - x }$
D) $f ( x ) = - 3 ^ { - x }$

Question 10

Approximate the number using a calculator. Round your answer to three decimal places.
The formula $S = A \left( \frac { ( 1 + r ) ^ { t + 1 } - 1 } { r } \right)$ models the value of a retirement account, where $A =$ the number of dollars added to the retirement account each year, $\mathrm { r } =$ the annual interest rate, and $\mathrm { S } =$ the value of the retirement account after t years. If the interest rate is $6 \%$ , how much will the account be worth after 15 years if $\$ 400$ is added each year? Round to the nearest whole number.

A) $\$ 10,269$
B) $\$ 999$
C) $\$ 6400$
D) $\$ 15,338$

Question 11

Graph the function
Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = 5 ^ { x } + 1$

A)

B)

C)

D)

Question 12

Approximate the number using a calculator. Round your answer to three decimal places.
$6 ^ { 3.6 }$

A) $632.914$
B) $21.600$
C) $2176.782$
D) $633.214$

Question 13

The graph of an exponential function is given. Select the function for the graph from the functions listed.

A) $f ( x ) = 5 ^ { x - 1 }$
B) $f ( x ) = 5 ^ { x }$
C) $f ( x ) = 5 ^ { x } - 1$
D) $f ( x ) = 5 ^ { x } + 1$

Question 14

Approximate the number using a calculator. Round your answer to three decimal places.
A city is growing at the rate of $0.7 \%$ annually. If there were $3,767,000$ residents in the city in 1992, find how many (to the nearest ten-thousand) are living in that city in 2000 . Use $y = 3,767,000 ( 2.7 ) = .007 \mathrm { t }$ .

A) $3,980,000$
B) 570,000
C) $10,170,000$
D) $4,010,000$

Question 15

The graph of an exponential function is given. Select the function for the graph from the functions listed.

A) $f ( x ) = 2 ^ { x }$
B) $f ( x ) = 2 ^ { x + 1 }$
C) $f ( x ) = 2 ^ { x } + 1$
D) $f ( x ) = 2 ^ { x } - 1$

Question 16

Approximate the number using a calculator. Round your answer to three decimal places.
$4 ^ { \pi }$

A) $77.880$
B) $97.409$
C) $12.566$
D) $36.462$

Question 17

Approximate the number using a calculator. Round your answer to three decimal places.
$6 ^{\sqrt { 2 }}$

A) $12.603$
B) $8.485$
C) $8.000$
D) $18.000$

Question 18

Graph the function by making a table of coordinates.
$f(x)=\left(\frac{3}{2}\right)^{x}$

A)

B)

C)

D)

Question 19

The graph of an exponential function is given. Select the function for the graph from the functions listed.

A) $f ( x ) = 2 ^ { - x }$
B) $f ( x ) = 2 ^ { x }$
C) $f ( x ) = - 2 ^ { x }$
D) $f ( x ) = - 2 ^ { - x }$

Question 20

Approximate the number using a calculator. Round your answer to three decimal places.
The function $f ( x ) = 500 ( 0.5 ) ^ { x / 100 }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $x$ is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 140 years. Round to the nearest whole number.

A) 189 pounds
B) 305 pounds
C) 350 pounds
D) 179 pounds

Question 21

Approximate the number using a calculator. Round your answer to three decimal places.
$\mathrm { e } ^ { 3.4 }$

A) $29.964$
B) $9.242$
C) $27.843$
D) $30.264$

Question 22

Graph the function
Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = 4 ^ { - x }$ .

A)

B)

C)

D)

Question 23

Graph the function
$$\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { x - 3 } + 4$$

A)

B)

C)

D)

Question 24

Approximate the number using a calculator. Round your answer to three decimal places.
$\mathrm { e } ^ { - 1.5 }$

A) $0.223$
В) $- 4.077$
C) $- 0.223$
D) $0.523$

Question 25

Graph the function
Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = 4 e ^ { x }$ .

A)

B)

C)

D)

Question 26

Graph the function
$$\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = \frac { 1 } { 3 } e ^ { x } \text {. }$$

A)

B)

C)

D)

Question 27

Graph the function
Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = \frac { 1 } { 4 } \cdot 4 ^ { x }$ .

A)

B)

C)

D)

Question 28

Graph the function
Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { 4 x }$ .

A)

B)

C)

D)

Question 29

Graph the function
Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = - 3 ^ { x }$ .

A)

B)

C)

D)

Question 30

Graph the function
Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { x + 4 }$ .

A)

B)

C)

D)

Question 31

Approximate the number using a calculator. Round your answer to three decimal places.
The function $\mathrm { D } ( \mathrm { h } ) = 8 \mathrm { e } ^ { - 0.4 \mathrm {~h} }$ can be used to determine the milligrams $\mathrm { D }$ of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 7 hours?

A) $0.49 \mathrm { mg }$
B) $131.56 \mathrm { mg }$
C) $5.81 \mathrm { mg }$
D) $0.29 \mathrm { mg }$

Question 32

Graph the function
Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x + 3 } + 2$

A)

B)

C)

D)

Question 33

Approximate the number using a calculator. Round your answer to three decimal places.
The population in a particular country is growing at the rate of $2.2 \%$ per year. If $6,365,000$ people lived there in 1999 , how many will there be in the year 2005 ? Use $\mathrm { f } ( \mathrm { x } ) = \mathrm { y } _ { 0 } \mathrm { e } ^ { 0.022 \mathrm { t } }$ and round to the nearest ten-thousand.

A) $7,260,000$
B) $7,990,000$
C) $7,120,000$
D) $8,720,000$

Question 34

Graph the function
$$\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { x } - 3$$

A)

B)

C)

D)

Question 35

Graph the function
$$\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { - x }$$

A)

B)

C)

D)

Question 36

Approximate the number using a calculator. Round your answer to three decimal places.
A sample of $400 \mathrm {~g}$ of lead-210 decays to polonium-210 according to the function given by $\mathrm { A } ( \mathrm { t } ) = 400 \mathrm { e } ^ { - 0.032 \mathrm { t } }$ , where $\mathrm { t }$ is time in years. What is the amount of the sample after 30 years (to the nearest g)?

A) $153 \mathrm {~g}$
B) $1045 \mathrm {~g}$
C) $83 \mathrm {~g}$
D) $111 \mathrm {~g}$

Question 37

Approximate the number using a calculator. Round your answer to three decimal places.
The size of the bear population at a national park increases at the rate of $4.8 \%$ per year. If the size of the current population is 152 , find how many bears there should be in 4 years. Use the function $f ( x ) = 152 e ^ { 0.048 t }$ and round to the nearest whole number.

A) 184
B) 186
C) 182
D) 188

Question 38

Graph the function
Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = 4 \cdot 4 ^ { x }$ .

A)

B)

C)

D)

Question 39

Graph the function
$$\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { x / 2 } - 1$$

A)

B)

C)

D)

Question 40

Graph the function
$$\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = - e ^ { x } \text {. }$$

A)

B)

C)

D)

Question 41

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
Find the accumulated value of an investment of $2000 at 4% compounded annually for 14 years.

A) $3463.35
B) $3330.15
C) $3040.00
D) $3120.00

Question 42

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
Suppose that you have $4000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?

A) $4000 invested at 6.25% compounded continuously over 10 years yields the greater return.
B) $4000 invested at 6.3% compounded semiannually over 10 years yields the greater return.
C) Both investment plans yield the same return.

Question 43

Write the equation in its equivalent exponential form.
$\log _ { 2 } 8 = 3$

A) $23 = 8$
B) $32 = 8$
C) $28 = 3$
D) $83 = 2$

Question 44

Write the equation in its equivalent exponential form.
$\log _ { 5 } x = 2$

A) $5 ^ { 2 } = x$
B) $25 = x$
C) $5 x = 2$
D) $x ^ { 2 } = 5$ x

Question 45

Write the equation in its equivalent logarithmic form.
$$9 ^ { x } = 729$$

A) $\log _ { 9 } 729 = \mathrm { x }$
B) $\log _ { x } 729 = 9$
C) $\log _ { 729 } 9 = \mathrm { x }$
D) $\log _ { 729 } x = 9$

Question 46

Write the equation in its equivalent logarithmic form.
$$3 - 2 = \frac { 1 } { 9 }$$

A) $\log _ { 3 } \frac { 1 } { 9 } = - 2$
B) $\log _ { 1 / 3 } 3 = - 2$
C) $\log _ { - 2 } \frac { 1 } { 9 } = 3$
D) $\log _ { 3 } - 2 = \frac { 1 } { 9 }$

Question 47

Write the equation in its equivalent exponential form.
$\log _ { b } 32 = 5$

A) $b ^ { 5 } = 32$
B) $5 ^ { \mathrm { b } } = 32$
C) $32 ^ { 5 } = \mathrm { b }$
D) $32 ^ { b } = 5$ 2

Question 48

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
Suppose that you have $10,000 to invest. Which investment yields the greater return over 9 years: 5.4% compounded monthly or 5.5% compounded quarterly?

A) $10,000 invested at 5.5% compounded quarterly over 9 years yields the greater return.
B) $10,000 invested at 5.4% compounded monthly over 9 years yields the greater return.
C) Both investment plans yield the same return.

Question 49

Write the equation in its equivalent logarithmic form.
$$43 = 64$$

A) $\log _ { 4 } 64 = 3$
B) $\log _ { 64 } 4 = 3$
C) $\log _ { 3 } 64 = 4$
D) $\log _ { 4 } 3 = 64$

Question 50

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
Find the accumulated value of an investment of $1020 at 6% compounded annually for 19 years.

A) $3086.11
B) $2911.43
C) $2121.60
D) $2182.80

Question 51

Write the equation in its equivalent logarithmic form.
$$2 ^ { 3 } = x$$

A) $\log _ { 2 } x = 3$
B) $\log _ { x } 2 = 3$
C) $\log _ { 3 } x = 2$
D) $\log _ { 2 } 3 = x$

Question 52

Evaluate the expression without using a calculator.
$\log _ { 5 } 25$

A) 2
B) 10
C) $\frac { 1 } { 2 }$
D) 1

Question 53

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
Find the accumulated value of an investment of $12,000 at 8% compounded semiannually for 11 years.

A) $28,439.03
B) $27,979.67
C) $18,473.45
D) $22,560.00

Question 54

Write the equation in its equivalent logarithmic form.
$$10 ^ { 3 } = y$$

A) $\log _ { 10 } y = 3$
B) $\log _ { 3 } y = 10$
C) $\log _ { \mathrm { y } } 10 = 3$
D) $\log _ { \mathrm { y } } 3 = 10$

Question 55

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years.

A) $7452.93
B) $12,911.25
C) $9093.60
D) $8060.16

Question 56

Write the equation in its equivalent logarithmic form.
$$\sqrt [ 3 ] { 8 } = 2$$

A) $\log _ { 8 } 2 = \frac { 1 } { 2 }$
B) $\log _ { 2 } 8 = \frac { 1 } { 2 }$
C) $\log _ { 8 } 3 = \frac { 1 } { 2 }$
D) $\log _ { 2 } 8 = 3$

Question 57

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
Find the accumulated value of an investment of $1400 at 8% compounded quarterly for 4 years.

A) $1921.90
B) $1904.68
C) $1515.41
D) $1848.00

Question 58

Write the equation in its equivalent exponential form.
$$\log _ { 3 } 9 = x$$

A) $3 ^ { x } = 9$
B) $x ^ { 3 } = 9$
C) $9 ^ { x } = 3$
D) $9 ^ { 3 } = \mathrm { x }$

Question 59

Write the equation in its equivalent logarithmic form.
$$b ^ { 2 } = 64$$

A) $\log _ { b } 64 = 2$
B) $\log _ { 64 } b = 2$
C) $\log _ { 2 } 64 = b$
D) $\log _ { \mathrm { b } } 2 = 64$

Question 60

Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
Find the accumulated value of an investment of $6000 at 8% compounded continuously for 4 years.

A) $8262.77
B) $8362.77
C) $8162.93
D) $7920.00

Question 61

Evaluate the expression without using a calculator.
$\log _ { 9 } 9$

A) 1
B) 9
C) $\frac { 1 } { 9 }$
D) 0

Question 62

Graph the function.
$$\text { Use the graph of } \log _ { 5 } x \text { to obtain the graph of } f ( x ) = 2 + \log _ { 5 } x \text {. }$$

A)

B)

C)

D)

Question 63

Evaluate the expression without using a calculator.
$\log _ { 5 } \frac { 1 } { 125 }$

A) $- 3$
B) 15
C) $\frac { 1 } { 3 }$
D) 3

Question 64

Graph the function.
Use the graph of $\log _ { 3 } x$ to obtain the graph of $f ( x ) = \log _ { 3 } ( x + 1 )$ .

A)

B)

C)

D)

Question 65

The graph of a logarithmic function is given. Select the function for the graph from the options.

A) $f ( x ) = \log _ { 3 } ( - x )$
B) $f ( x ) = - \log _ { 3 } x$
C) $f ( x ) = 1 - \log _ { 3 } x$
D) $f ( x ) = \log _ { 3 } x$

Question 66

Evaluate the expression without using a calculator.
$\log _ { 8 } 8 ^ { 13 }$

A) 13
B) 8
C) 21
D) $\log _ { 8 } 13$

Question 67

Evaluate the expression without using a calculator.
$\log _ { 5 } \frac { 1 } { 5 }$

A) $- 1$
B) 5
C) $- 5$
D) 1

Question 68

The graph of a logarithmic function is given. Select the function for the graph from the options.

A) $f ( x ) = \log _ { 4 } x$
B) $f ( x ) = \log _ { 4 } ( x + 1 )$
C) $f ( x ) = \log _ { 4 } ( x - 1 )$
D) $f ( x ) = \log _ { 4 } x + 1$

Question 69

The graph of a logarithmic function is given. Select the function for the graph from the options.

A) $f ( x ) = \log _ { 3 } ( x + 2 )$
B) $f ( x ) = \log _ { 3 } x$
C) $f ( x ) = \log _ { 3 } ( x - 2 )$
D) $f ( x ) = \log _ { 3 } x + 2$

Question 70

Evaluate the expression without using a calculator.
$\log _ { 3 } \frac { 1 } { \sqrt { 3 } }$

A) $- \frac { 1 } { 2 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 3 }$
D) $- \frac { 1 } { 3 }$

Question 71

Evaluate the expression without using a calculator.
$\log _ { 5 } \sqrt { 5 }$

A) $\frac { 1 } { 2 }$
B) 5
C) $\frac { 1 } { 5 }$
D) 1

Question 72

Graph the function.
Use the graph of log2 x to obtain the graph of f(x) = -2 log2 x.

A)

B)

C)

D)

Question 73

The graph of a logarithmic function is given. Select the function for the graph from the options.

A) $f ( x ) = 1 - \log _ { 4 } x$
B) $f ( x ) = \log _ { 4 } ( - x )$
C) $f ( x ) = - \log _ { 4 } x$
D) $f ( x ) = \log _ { 4 } x$

Question 74

The graph of a logarithmic function is given. Select the function for the graph from the options.

A) $f ( x ) = \log _ { 4 } x - 2$
B) $f ( x ) = \log _ { 4 } x$
C) $f ( x ) = \log _ { 4 } ( x + 2 )$
D) $f ( x ) = \log _ { 4 } ( x - 2 )$

Question 75

Evaluate the expression without using a calculator.
$\log _ { 10 } 1000$

A) 3
B) 30
C) $\frac { 1 } { 1000 }$
D) $- 3$

Question 76

Evaluate the expression without using a calculator.
$\log _ { 64 } 4$

A) $\frac { 1 } { 3 }$
B) 12
C) 3
D) 1

Question 77

Evaluate the expression without using a calculator.
$\log _ { 5 } 625$

A) 4
B) 625
C) 20
D) 5

Question 78

Evaluate the expression without using a calculator.
${ } _ { 3 } \log _ { 3 } 18$

A) 18
B) 3
C) 21
D) $\log _ { 3 } 18$

Question 79

Evaluate the expression without using a calculator.
$\log _ { 11 } 1$

A) 0
B) 11
C) $\frac { 1 } { 11 }$
D) 1

Question 80

The graph of a logarithmic function is given. Select the function for the graph from the options.

A) $f ( x ) = - \log _ { 4 } x$
B) $f ( x ) = \log _ { 4 } ( - x )$
C) $f ( x ) = 1 - \log _ { 4 } x$
D) $f ( x ) = \log _ { 4 } x$