Deck 4: Exponential and Logarithmic Functions

Question 1

Solve the problem.
A city is growing at the rate of 0.3% annually. If there were 2,520,000 residents in the city in 1993, find how many (to the nearest ten-thousand)are living in that city in 2000. Use y = 2,520,000(2.7)0.003t.

A)2,570,000
B)140,000
C)6,800,000
D)2,600,000

Answer 1

A

Question 2

Graph the function.
Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = 5 ^ { x - 4 }$

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

Answer 3

A

Question 4

Solve the problem.
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 $7 \%$ , how much will the account be worth after 15 years if $\$ 800$ is added each year? Round to the nearest whole number.

A) $\$ 22,310$
B) $\$ 2347$
C) $\$ 12,800$
D) $\$ 35,316$

Question 5

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

A) $f ( x ) = - 4 ^ { - x }$
B) $f ( x ) = 4 ^ { x }$
C) $f ( x ) = - 4 ^ { x }$
D) $f ( x ) = 4 ^ { - x }$

Question 6

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 7

Graph the function by making a table of coordinates.
$f(x)=\left(\frac{1}{3}\right)^{x}$

A)

B)

C)

D)

Question 8

Solve the problem.
The rabbit population in a forest area grows at the rate of $4 \%$ monthly. If there are 190 rabbits in July, find how many rabbits (rounded to the nearest whole number) should be expected by next July. Use $y = 190 ( 2.7 ) ^ { 0.04 t }$

A) 306
B) 246
C) 319
D) 293

Question 9

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

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

Question 10

Approximate the number using a calculator. Round your answer to three decimal places.
$2 ^ { - 1.3 }$

A) $0.406$
B) $- 2.600$
C) $1.690$
D) $0.706$

Question 11

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

A)

B)

C)

D)

Question 12

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

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

Question 13

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

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

Question 14

Approximate the number using a calculator. Round your answer to three decimal places.
$3.2 \pi$

A) $38.635$
B) $38.983$
C) $10.053$
D) $36.462$

Question 15

Approximate the number using a calculator. Round your answer to three decimal places.
$6 ^ { 3.3 }$

A) $369.742$
B) $19.800$
C) $1291.468$
D) $370.042$

Question 16

Approximate the number using a calculator. Round your answer to three decimal places.
$2 ^ { \sqrt { 3 } }$

A) $3.322$
B) $3.464$
C) $3.000$
D) $4.000$

Question 17

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

A)

B)

C)

D)

Question 18

Graph the function by making a table of coordinates.
$$f ( x ) = 0.2 ^ { x }$$

A)

B)

C)

D)

Question 19

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

A)

B)

C)

D)

Question 20

Solve the problem.
The function $f ( x ) = 300 ( 0.5 ) ^ { x / 100 }$ 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 120 years. Round to the nearest whole number.

A) 131 pounds
B) 168 pounds
C) 180 pounds
D) 125 pounds

Question 21

Solve the problem.
The size of the bear population at a national park increases at the rate of $4.6 \%$ per year. If the size of the current population is 157 , find how many bears there should be in 6 years. Use the function $f ( x ) = 157 e ^ { 0.046 t }$ and round to the nearest whole number.

A) 207
B) 209
C) 205
D) 211

Question 22

Graph the function.
Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { x - 5 }$

A)

B)

C)

D)

Question 23

Solve the problem.
The function $\mathrm { D } ( \mathrm { h } ) = 9 \mathrm { e } ^ { - 0.4 \mathrm {~h} }$ 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 11 hours?

A) $0.11 \mathrm { mg }$
B) $733.06 \mathrm { mg }$
C) $5.57 \mathrm { mg }$
D) $0.30 \mathrm { mg }$

Question 24

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 25

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

A)

B)

C)

D)

Question 26

Graph the function.
Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x + 2 } + 1$

A)

B)

C)

D)

Question 27

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 28

Approximate the number using a calculator. Round your answer to three decimal places.
$\mathrm { e } ^ { 3.2 }$

A) $24.533$
B) $8.699$
C) $23.612$
D) $24.833$

Question 29

Solve the problem.
The population in a particular country is growing at the rate of $1.7 \%$ per year. If $7,638,000$ people lived there in 1999 , how many will there be in the year 2004 ? Use $f ( x ) = y _ { 0 } e ^ { 0.017 t }$ and round to the nearest ten-thousand.

A) $8,320,000$
B) $9,150,000$
C) $8,150,000$
D) $9,980,000$

Question 30

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

A)

B)

C)

D)

Question 31

Approximate the number using a calculator. Round your answer to three decimal places.
$\mathrm { e } ^ { - 2.1 }$

A) $0.122$
B) $- 5.708$
C) $- 0.122$
D) $0.422$

Question 32

Graph the function.
Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { 6 x }$ .

A)

B)

C)

D)

Question 33

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

A)

B)

C)

D)

Question 34

Graph the function.
Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = \frac { 1 } { 2 } \cdot 2 ^ { x }$ .

A)

B)

C)

D)

Question 35

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

A)

B)

C)

D)

Question 36

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 37

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

A)

B)

C)

D)

Question 38

Solve the problem.
A sample of $300 \mathrm {~g}$ of lead-210 decays to polonium-210 according to the function given by $\mathrm { A } ( \mathrm { t } ) = 300 \mathrm { e } ^ { - 0.032 \mathrm { t } }$ , where $\mathrm { t }$ is time in years. What is the amount of the sample after 60 years (to the nearest g)?

A) $44 \mathrm {~g}$
B) $2046 \mathrm {~g}$
C) $230 \mathrm {~g}$
D) $32 \mathrm {~g}$

Question 39

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 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 Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
Suppose that you have $11,000 to invest. Which investment yields the greater return over 9 years: 7.5% compounded continuously or 7.6% compounded semiannually?

A)$11,000 invested at 7.5% compounded continuously over 9 years yields the greater return.
B)$11,000 invested at 7.6% compounded semiannually over 9 years yields the greater return.
C)Both investment plans yield the same return.

Question 42

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

A) $b ^ { 3 } = 8$
B) $3 ^ { b } = 8$
C) $8 ^ { 3 } = b$
D) $8 ^ { b } = 3$

Question 43

Write the equation in its equivalent exponential form.
$$\log _ { 6 } 216 = x$$

A) $6 ^ { x } = 216$
B) $x ^ { 6 } = 216$
C) $216 ^ { x } = 6$
D) $216 ^ { 6 } = x$

Question 44

Write the equation in its equivalent logarithmic form.
$$5 - 2 = \frac { 1 } { 25 }$$

A) $\log _ { 5 } \frac { 1 } { 25 } = - 2$
B) $\log _ { 1 / 5 } 5 = - 2$
C) $\log _ { - 2 } \frac { 1 } { 25 } = 5$
D) $\log _ { 5 } - 2 = \frac { 1 } { 25 }$

Question 45

Write the equation in its equivalent logarithmic form.
$$c ^ { 4 } = 20,736$$

A) $\log _ { \mathrm { C } } 20,736 = 4$
B) $\log _ { 20,736 } \mathrm { c } = 4$
C) $\log _ { 4 } 20,736 = c$
D) $\log _ { \mathrm { C } } 4 = 20,736$

Question 46

Write the equation in its equivalent logarithmic form.
$$72 = 49$$

A) $\log _ { 7 } 49 = 2$
B) $\log _ { 49 } 7 = 2$
C) $\log _ { 2 } 49 = 7$
D) $\log _ { 7 } 2 = 49$

Question 47

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
Find the accumulated value of an investment of $19,000 at 8% compounded annually for 10 years.

A)$41,019.57
B)$37,981.09
C)$32,680.00
D)$34,200.00

Question 48

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
Find the accumulated value of an investment of $6000 at 7% compounded continuously for 5 years.

A)$8514.41
B)$8614.41
C)$8415.31
D)$8100.00

Question 49

Write the equation in its equivalent logarithmic form.
$$72 = x$$

A) $\log _ { 7 } x = 2$
B) $\log _ { x } 7 = 2$
C) $\log _ { 2 } x = 7$
D) $\log _ { 7 } 2 = x$

Question 50

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
Find the accumulated value of an investment of $2000 at 10% compounded semiannually for 7 years.

A)$3959.86
B)$3897.43
C)$2814.20
D)$3400.00

Question 51

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
Suppose that you have $10,000 to invest. Which investment yields the greater return over 6 years: 5.4% compounded monthly or 5.5% compounded quarterly?

A)$10,000 invested at 5.5% compounded quarterly over 6 years yields the greater return.
B)$10,000 invested at 5.4% compounded monthly over 6 years yields the greater return.
C)Both investment plans yield the same return.

Question 52

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
Find the accumulated value of an investment of $1230 at 6% compounded annually for 5 years.

A)$1646.02
B)$1552.85
C)$1525.20
D)$1599.00

Question 53

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

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

Question 54

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
Find the accumulated value of an investment of $900 at 10% compounded quarterly for 5 years.

A)$1474.75
B)$1449.46
C)$1018.27
D)$1350.00

Question 55

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
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 exponential form.
$\log _ { 5 } x = 3$

A) $5 ^ { 3 } = x$
B) $35 = x$
C) $5 x = 3$
D) $x ^ { 3 } = 5$

Question 57

Evaluate the expression without using a calculator.
$\log _ { 2 } 4$

A) 2
B) 4
C) $\frac { 1 } { 2 }$
D) 1

Question 58

Write the equation in its equivalent logarithmic form.
$$13 ^ { 2 } = y$$

A) $\log _ { 13 } \mathrm { y } = 2$
B) $\log _ { 2 } y = 13$
C) $\log _ { y } 13 = 2$
D) $\log _ { y } 2 = 13$

Question 59

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

A) $2 ^ { 3 } = 8$
B) $3 ^ { 2 } = 8$
C) $28 = 3$
D) $8 ^ { 3 } = 2$

Question 60

Write the equation in its equivalent logarithmic form.
$$13 ^ { x } = 169$$

A) $\log _ { 13 } 169 = x$
B) $\log _ { \mathrm { x } } 169 = 13$
C) $\log _ { 169 } 13 = x$
D) $\log _ { 169 } x = 13$

Question 61

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

A) $f ( x ) = \log _ { 5 } ( - x )$
B) $f ( x ) = - \log _ { 5 } x$
C) $f ( x ) = 1 - \log _ { 5 } x$
D) $f ( x ) = \log _ { 5 } x$

Question 62

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

A) $\frac { 1 } { 2 }$
B) 8
C) $\frac { 1 } { 8 }$
D) 1

Question 63

Evaluate the expression without using a calculator.
$8 ^ { \log _ { 8 } 18 }$

A) 18
B) 8
C) 26
D) $\log _ { 8 } 18$

Question 64

Evaluate the expression without using a calculator.
$\log _ { 12 } 1$

A) 0
B) 12
C) $\frac { 1 } { 12 }$
D) 1

Question 65

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

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

Question 66

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

A)

B)

C)

D)

Question 67

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

A)

B)

C)

D)

Question 68

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 69

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

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

Question 70

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

A) 1
B) 10
C) $\frac { 1 } { 10 }$
D) 0

Question 71

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

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

Question 72

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

A) $f ( x ) = 1 - \log _ { 5 } x$
B) $f ( x ) = \log _ { 5 } ( - x )$
C) $f ( x ) = - \log _ { 5 } x$
D) $f ( x ) = \log _ { 5 } x$

Question 73

Evaluate the expression without using a calculator.
$\log _ { 16 } 4$

A) $\frac { 1 } { 2 }$
B) 8
C) 2
D) 1

Question 74

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

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

Question 75

Evaluate the expression without using a calculator.
$\log _ { 3 } 81$

A) 4
B) 81
C) 12
D) 3

Question 76

Evaluate the expression without using a calculator.
$\log _ { 8 } \frac { 1 } { 8 }$

A) $- 1$
B) 8
C) $- 8$
D) 1 )1

Question 77

Evaluate the expression without using a calculator.
$$\log _ { 4 } \frac { 1 } { 16 }$$

A) $- 2$
B) 8
C) $\frac { 1 } { 2 }$
D) 2

Question 78

Graph the function.
Use the graph of $\log _ { 2 } x$ to obtain the graph of $f ( x ) = 1 + \log _ { 2 } x$ .

A)

B)

C)

D)

Question 79

Evaluate the expression without using a calculator.
$\log 10 \frac { 1 } { \sqrt { 10 } }$

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

Question 80

Evaluate the expression without using a calculator.
$\log _ { 8 } 8 ^ { 19 }$

A) 19
B) 8
C) 27
D) $\log _ { 8 } 19$