Deck 4: Exponential and Logarithmic Functions

Question 1

Classify the function as a linear, quadratic, or exponential.

-f $(x)=-4 x-2$

A) Linear
B) Exponential
C) Quadratic

Answer 1

Linear

Question 2

Classify the function as a linear, quadratic, or exponential.

- $f(x)=-x$

A) Quadratic
B) Exponential
C) Linear

Answer 2

Linear

Question 3

Classify the function as a linear, quadratic, or exponential.

- $f(x)=x^{2}+8$

A) Exponential
B) Quadratic
C) Linear

Answer 3

Quadratic

Question 4

Classify the function as a linear, quadratic, or exponential.

- $f(x)=-6 x^{2}-5 x-6$

A) Exponential
B) Quadratic
C) Linear

Question 5

Classify the function as a linear, quadratic, or exponential.

- $f(x)=(x-4)(x+9)$

A) Linear
B) Exponential
C) Quadratic

Question 6

Classify the function as a linear, quadratic, or exponential.

- $f(x)=2^{x-7}$

A) Exponential
B) Quadratic
C) Linear

Question 7

Classify the function as a linear, quadratic, or exponential.

- $f(x)=8 \cdot 54 x^{2}-3$

A) Quadratic
B) Linear
C) Exponential

Question 8

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$

- $f(x)=0.6^{x}$

A) The graph lies below the $x$ -axis, falls from right to left, with the positive $x$ -axis as a horizontal asymptote; $(0,0.6)$ and $(1,6)$ .
B) The graph lies below the $x$ -axis, falls from left to right, with the positive $x$ -axis as a horizontal asymptote; $(0,1)$ and $(1,0.6)$ .
C) The graph lies above the $x$ -axis, falls from right to left, with the positive $x$ -axis as a horizontal asymptote; $(0,0.6)$ and $(1,6)$ .
D) The graph lies above the $x$ -axis, falls from left to right, with the positive $x$ -axis as a horizontal asymptote; $(0,1)$ and $(1,0.6)$ .

Question 9

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$

- $f(x)=-\left(3^{x}\right)$

A) The graph lies below the $x$ -axis, falls from left to right, with the negative $x$ -axis as a horizontal asy mptote; $(0,-1)$ and $(1,-3)$ .
B) The graph lies above the $x$ -axis, falls from right to left, with the negative $x$ -axis as a horizontal asymptote; $(0,-3)$ and $(1,3)$ .
C) The graph lies below the $x$ -axis, falls from right to left, with the negative $x$ -axis as a horizontal asymptote; $(0,-3)$ and $(1,3)$ .
D) The graph lies above the $x$ -axis, falls from left to right, with the negative $x$ -axis as a horizontal asymptote; $(0,1)$ and $(1,-3)$ .

Question 10

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$

- $f(x)=6^{-x}$

A) The graph lies above the $x$ -axis, falls from left to right, with the positive $x$ -axis as a horizontal asymptote; $(0,1)$ and $\left(1, \frac{1}{6}\right)$ .
B) The graph lies above the $x$ -axis, falls from left to right, with the negative $x$ -axis as a horizontal asymptote; $(0,1)$ and $\left(1,-\frac{1}{6}\right)$ .
C) The graph lies above the $x$ -axis, falls from right to left, with the negative $x$ -axis as a horizontal asymptote; $(0,6)$ and $\left(1,-\frac{1}{6}\right)$ .
D) The graph lies above the $x$ -axis, falls from right to left, with the positive $x$ -axis as a horizontal asymptote; $(0,6)$ and $\left(1, \frac{1}{6}\right)$ .

Question 11

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$

- $f(x)=7^{0.4 x}$

A) The graph lies above the $x$ -axis, falls from left to right, with the negative $x$ -axis as a horizontal asymptote; $(0,7)$ and $\left(1,7^{0.4}\right)$ .
B) The graph lies below the $x$ -axis, rises from left to right, with the negative $x$ -axis as a horizontal asymptote; $(0,1)$ and $\left(1,7^{4}\right)$ .
C) The graph lies above the $x$ -axis, rises from left to right, with the negative $x$ -axis as a horizontal asymptote; $(0,1)$ and $\left(1,7^{0.4}\right)$ .
D) The graph lies below the $x$ -axis, falls from right to left, with the negative $x$ -axis as a horizontal asymptote; $(0,7)$ and $\left(1,7^{4}\right)$ .

Question 12

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$

- $f(x)=4^{2 x}$

A) The graph lies below the $x$ -axis, falls from right to left, with the positive $x$ -axis as a horizontal asymptote; $(0,4)$ and $(1,16)$ .
B) The graph lies above the $x$ -axis, rises from right to left, with the negative $x$ -axis as a horizontal asymptote; $(0,4)$ and $(1,16)$ .
C) The graph lies above the $x$ -axis, rises from left to right, with the negative $x$ -axis as a horizontal asymptote; $(0,4)$ and $(1,16)$ .
D) The graph lies below the $x$ -axis, falls from left to right, with the positive $x$ -axis as a horizontal asymptote; $(0,1)$ and $(1,-16)$ .

Question 13

Graph the function.

- $f(x)=4^{x}$

A)
B)
C)
D)

Question 14

Graph the function.

- $f(x)=\left(\frac{1}{5}\right)^{x}$

A)
B)
C)
D)

Question 15

Graph the function.

- $f(x)=3^{-x}$

A)
B)
C)
D)

Question 16

Graph the function.

- $f(x)=4^{(4 x-2)}$

A)
B)
C)
D)

Question 17

Graph the function.

- $f(x)=2(x-2)$

A)
B)
C)
D)

Question 18

Graph the function.

- $f(x)=\left(\frac{1}{5}\right)^{x}+1$

A)
B)
C)
D)

Question 19

Graph the function.

- $f(x)=0.7^{x}$

A)
B)
C)
D)

Question 20

Graph the function.

- $f(x)=-\left(3^{x}\right)$

A)
B)
C)
D)

Question 21

Graph the function.

- $f(x)=2^{-x^{2}}$

A)
B)
C)
D)

Question 22

Graph the function.

- $f(x)=e^{3 x}-4$

A)
B)
C)
D)

Question 23

Provide an appropriate response.

-In the given figure, the graphs of $y=a^{x}$ for $a=1.5,2.3,3.4,0.6,0.87,0.42$ are given. Identify the graph of $\mathrm{y}=2.3^{\mathrm{x}}$ .

A) V
B) III
C) VI
D) I

Question 24

Provide an appropriate response.

-The graph of an exponential function is given. Which of the following is the correct equation of the function?

A) $y=0.31^{x}$
B) $y=2.4^{x}$
C) $\mathrm{y}=1.8^{\mathrm{x}}$
D) $y=0.45^{x}$

Question 25

Provide an appropriate response.

-The graph of an exponential function is given. Which of the following is the correct equation of the function?

A)
B) $y=2.4^{x}$
C) $y=0.65^{x}$
D) $y=0.32^{x}$

Question 26

Provide an appropriate response.

-The graph of an exponential function is given. Which of the following is the correct equation of the function?

A) $y=0.45^{x}$
B) $y=3.9^{x}$
C) $\mathrm{y}=2.8^{\mathrm{x}}$
D) $y=0.73^{x}$

Question 27

Provide an appropriate response.

-The graph of an exponential function is given. Which of the following is the correct equation of the function?

A) $y=0.74^{x}$
B) $\mathrm{y}=1.9^{\mathrm{x}}$
C) $y=3.6^{x}$
D) $y=0.26^{x}$

Question 28

Write the word or phrase that best completes each statement or answers the question.

- $f(x)=a^{x}$
The graph of an exponential function with base a is given. Is a $>1$ or is $0<a<1$ ? Explain how you arrived at your answer. Give the domain and range of $\mathrm{f}$ .

Question 29

Write the word or phrase that best completes each statement or answers the question.

- $f(x)=a^{x}$
The graph of an exponential function with base $a$ is given. Sketch the graph of $g(x)=-a^{x}$ . Give the domain and range of $g$ .

Question 30

Write the word or phrase that best completes each statement or answers the question.

- $f(x)=a^{x}$
The graph of an exponential function with base a is given. Sketch the graph of $h(x)=a^{-x}$ . Give the domain and range of $h$ .

Question 31

Write the word or phrase that best completes each statement or answers the question.

- $f(x)=a^{x}$
The graph of an exponential function with base a is given. Sketch the graph of $g(x)=a^{x}+2$ . Give the domain and range of $g$ .

Question 32

Write the word or phrase that best completes each statement or answers the question.

- $f(x)=a^{x}$
The graph of an exponential function with base a is given. Sketch the graph of $g(x)=a^{x+2}$ . Give the domain and range of $g$ .

Question 33

Solve the problem.

-An economist predicts that the buying power $B(x)$ of a dollar $x$ years from now will decrease according to the formula $\mathrm{B}(\mathrm{x})=0.42^{\mathrm{x}}$ . How much will today's dollar be worth in 5 years? Round the answer to the nearest cent.

A)\$ 1.97
B) $\$ 0.65$
C) $\$ 2.10$
D) $\$ 0.01$

Question 34

Solve the problem.

-The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by $\mathrm{D}(\mathrm{x})=3700(2)^{\mathrm{x}}$ , where $\mathrm{x}$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $x=0$ and $x=4$ .

A) $7400,59,200$
B) $3700,59,200$
C) $3700,14,800$
D) $3700,29,600$

Question 35

Solve the problem.

-The number of dislocated electric impulses per cubic inch in a transformer when lightning strikes is given by $D(x)=5400(4)^{x}$ , where $x$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $\mathrm{x}=0$ and $\mathrm{x}=5$ .

A) $21,600,5,529,600$
B) $5400,1,382,400$
C) $5400,5,529,600$
D) $5400,108,000$

Question 36

Solve the problem.

-The amount of particulate matter left in solution during a filtering process is given by the equation $P(x)=200(2)^{-0.8 n}$ , where $n$ is the number of filtering steps. Find the amounts left for $\mathrm{n}=0$ and $\mathrm{n}=5$ . (Round to the nearest whole number.)

A) 200,13
B) 400,13
C) 200,6
D) 200,3200

Question 37

Solve the problem.

-The number of bacteria growing in an incubation culture increases with time according to $B(x)=4700(3)^{x}$ , where $x$ is time in days. Find the number of bacteria when $x=0$ and $x=5$ .

A) $4700,70,500$
B) $4700,126,900$
C) $14,100,1,142,100$
D) $4700,1,142,100$

Question 38

Solve the problem.

-Suppose the amount of a radioactive element remaining in a sample of 100 milligrams after $x$ years can be described by $\mathrm{A}(\mathrm{x})=100 \mathrm{e}^{-0.01679 \mathrm{x}}$ . How much is remaining after 194 years? Round the answer to the nearest hundredth of a milligram.

A) 0.04 milligrams
B) 2597.83 milligrams
C) 325.73 milligrams
D) 3.85 milligrams

Question 39

Solve the problem.

-The decay of $289 \mathrm{mg}$ of an isotope is given by $A(t)=289 e^{-0.027 t}$ , where $t$ is time in years. Find the amount left after 4 years.

A) 259
B) 253
C) 130
D) 281

Question 40

Solve the problem.

-Use the formula $P=I e^{k t}$ . A bacterial culture has an initial population of 500. If its population grows to 7000 in 6 hours, what will it be at the end of 8 hours?

A) 4838
B) 51,714
C) 1117
D) 16,723

Question 41

Solve the problem.

-Use the formula $P=I e^{k t}$ . A bacterial culture has an initial population of 10,000 . If its population declines to 3000 in 2 hours, what will it be at the end of 4 hours?

A) 450
B) 900
C) 4481
D) 3500

Question 42

Solve the problem.

-The population of a particular city is increasing at a rate proportional to its size. It follows the function $\mathrm{P}(\mathrm{t})=1+\mathrm{ke}^{0.08 \mathrm{t}}$ where $\mathrm{k}$ is a constant and $\mathrm{t}$ is the time in years. If the current population is 29,000 , in how many years is the population expected to be 72,500 ?

A) 79 year(s)
B) 5 years(s)
C) 6 year(s)
D) 11 year(s)

Question 43

Solve the problem.

-The number of books in a small library increases according to the function $B=3700 \mathrm{e}^{0.05 t}$ , where $t$ is measured in years. How many books will the library have after 3 years?

A) 5226
B) 4299
C) 3048
D) 7019

Question 44

Solve the problem.

-The sales of a mature product (one which has passed its peak) will decline by the function $S(t)=S_{0} e^{-a t}$ , where $t$ is time in years. Find the sales after 9 years if $a=0.14$ and $S_{0}=56,100$ .

A) 7957
B) 227,497
C) 15,913
D) 64,530

Question 45

Solve the problem.

-The growth in the population of a certain rodent at a dump site fits the exponential function $A(t)=599 e^{0.02 t}$ , where $t$ is the number of years since 1967. Estimate the population in the year 2000.

A) 580
B) 1182
C) 1159
D) 611

Question 46

Solve the problem.

-The decay of $163 \mathrm{mg}$ of an isotope is given by $\mathrm{A}(\mathrm{t})=163 \mathrm{e}^{-0.014 \mathrm{t}}$ , where $\mathrm{t}$ is time in years. Find the amount left after 13 years.

A) 136
B) 161
C) 134
D) 68

Question 47

Find an exponential function of theform $P(t) = y_{0} e^{k t}$ to model the given data.

-Under ideal conditions, a population of rabbits has an exponential growth rate of $11.6 \%$ per day. Consider an initial population of 900 rabbits. Find the exponential growth function.

A)P $(t)=100 \mathrm{e}^{11.6 \mathrm{t}}$
B) $P(t)=100 e^{1.16 t}$
C)P $(t)=900 e^{0.116 t}$
D) $P(t)=90 e^{0.116 t}$

Question 48

Find an exponential function of theform $P(t) = y_{0} e^{k t}$ to model the given data.

-In 1985, the number of female athletes participating in Summer Olympic-Type Games was 550. In 1996, about 3550 participated in the Summer Olympics in Atlanta. Assuming that $P(0)=500$ and that the exponential model applies, find the value of $\mathrm{k}$ rounded to the hundredths place, and write the function.

A) $\mathrm{k}=0.17 ; \mathrm{P}(\mathrm{t})=500 \mathrm{e}^{0.17 \mathrm{t}}$
B) $\mathrm{k}=0.17 ; \mathrm{P}(\mathrm{t})=500 \mathrm{e}^{0.27 \mathrm{t}}$
C) $\mathrm{k}=0.19 ; \mathrm{P}(\mathrm{t})=500 \mathrm{e}^{0.19 \mathrm{t}}$
D) $k=0.16 ; \mathrm{P}(\mathrm{t})=500 \mathrm{e}^{0.16 \mathrm{t}}$

Question 49

Solve the problem.

-Use a graphing calculator to predict about how many books will have been read in the eighth grade.

A) 500
B) 1000
C) 3000
D) 2000

Question 50

Solve the problem.

-Use a graphing calculator to predict about how many widgets will be produced in 2004.

A) 11 million
B) 60 million
C) 20 million
D) 44 million

Question 51

Solve the problem.

-Use a graphing calculator to predict what income the company should expect in its seventh year of operation.

A) 5-7 million
B) 2-3 million
C) 30-40 million
D) 10-20 million

Question 52

Solve.

-In a town whose population is 3500 , a disease creates an epidemic. The number $\mathrm{N}$ of people infected $t$ days after the disease has begun is given by the function
$\mathrm{N}(\mathrm{t})=\frac{3500}{1+18 \cdot \mathrm{e}^{-0.8 \mathrm{t}}}$
Find the number infected after 16 days.

A) 3502
B) 3498
C) 3500
D) 3503

Question 53

Solve.

-In recent years, many states have passed laws against smoking in public buildings. The total number of states $\mathrm{N}$ that have passed a no smoking in public buildings law, $\mathrm{t}$ years after 1985 is given by the function
$\mathrm{N}(\mathrm{t})=\frac{50}{1+19 \mathrm{e}^{-0.4 \mathrm{t}}}$
How many states had passed the law in 1985 ?

A) 2.5
B) 1.25
C) 0.25
D) 0

Question 54

Solve.

-A lake is stocked with 578 fish of a new variety. The size of the lake, the availability of food, and the number of other fish restrict growth in the lake to a limiting value of 3612. The population of fish in the lake after time $t$ , in months, is given by the function
$$P(t)=\frac{3612}{1+4.98 \mathrm{e}^{-0.32 \mathrm{t}}} .$$
Find the population after 20 months.

A) 3597
B) 3582
C) 3572
D) 3592

Question 55

Convert to exponential form.

- $\log _{5} 125=3$

A) $(3)^{5}=125$
B) $(5)^{125}=3$
C) $(125)^{3}=5$
D) $(5)^{3}=125$

Question 56

Convert to exponential form.

- $\log _{5} \frac{1}{125}=-3$

A) $5^{125}=3$
B) $\left(\frac{1}{125}\right)^{3}=5$
C) $3^{5}=\frac{1}{125}$
D) $5^{-3}=\frac{1}{125}$

Question 57

Convert to exponential form.

- $\log _{4} 64=3$

A) $64^{3}=4$
B) $4^{64}=3$
C) $4^{3}=64$
D) $3^{4}=64$

Question 58

Convert to exponential form.

- $\log 0.000001=-6$

A) $10^{0.000001}=-6$
B) $0.000001^{-6}=10$
C) $-6^{10}=0.000001$
D) $10^{-6}=0.000001$

Question 59

Write in logarithmic form.

- $6^{2}=36$

A) $6=\log _{2} 36$
B) $2=\log _{6} 36$
C) $2=\log _{36} 6$
D) $36=\log _{6} 2$

Question 60

Write in logarithmic form.

- $2^{2}=4$

A) $4=\log _{2} 2$
B) $2=\log _{2} 4$
C) $2=\log _{2} 4$ .
D) $2=\log _{4} 2$

Question 61

Write in logarithmic form.

- $4^{-3}=\frac{1}{64}$

A) $-3=\log _{1 / 64} 4$
B) $\frac{1}{64}=\log _{4}-3$
C) $-3=\log _{4} \frac{1}{64}$
D) $4=\log _{-3} \frac{1}{64}$

Question 62

Write in logarithmic form.

- $6561^{1 / 4}=9$

A) $9=\log _{6561} \frac{1}{4}$
B) $\frac{1}{4}=\log _{6561} 9$
C) $\frac{1}{4}=\log _{9} 6561$
D) $9=\log _{1 / 4} 6561$

Question 63

Write in logarithmic form.

- $\mathrm{e}^{-2}=0.1353$

A) $-2=\log _{e} 0.1353$
B) $0.1353=\log _{e}-2$
C) $0.1353=\log _{-2} \mathrm{e}$
D) $e=\log _{-2} 0.1353$

Question 64

Find the value of the expression.

- $\log _{9} 9^{3}$

A) 27
B) 9
C) 3
D) 729

Question 65

Find the value of the expression.

- $\log _{5} 25$

A) 5
B) 10
C) 2
D) 25

Question 66

Find the value of the expression.

- $\log _{4} \frac{1}{4}$

A) 1
B) -1
C) 4
D) 0

Question 67

Find the value of the expression.

- $\log 9 \frac{1}{81}$

A) 9
B) -9
C) 2
D) -2

Question 68

Find the value of the expression.

- $\log _{10} 10$

A) -1
B) 1
C) 0
D) 10

Question 69

Find the value of the expression.

- $\log _{9} \frac{1}{729}$

A) 81
B) -3
C) 3
D) -81

Question 70

Find the value of the expression.

- $\log _{8} 32$

A) $\frac{4}{3}$
B) $\frac{5}{4}$
C) $\frac{3}{2}$
D) $\frac{5}{3}$

Question 71

Find the value of the expression.

-ln e

A) e
B) -1
C) 1
D) 0

Question 72

Find the value of the expression.

- $\ln 1$

A) 1
B) 0
C) $\mathrm{e}$
D) -1

Question 73

Use a calculator to evaluate the logarithm.

- $\log 280$

A) 2.4456
B) 2.4487
C) 5.6348
D) 2.4472

Question 74

Use a calculator to evaluate the logarithm.

- $\log 3.45$

A) 0.5250
B) 0.5378
C) 0.5502
D) 1.2384

Question 75

Use a calculator to evaluate the logarithm.

- $\log 4174$

A) 8.3366
B) 3.6216
C) 3.6195
D) 3.6206

Question 76

Use a calculator to evaluate the logarithm.

- $\log 0.0795$

A) -2.5320
B) -1.0942
C) -1.0996
D) -1.1051

Question 77

Use a calculator to evaluate the logarithm.

- $\log 0.00457$

A) -5.3882
B) -2.3497
C) -2.3307
D) -2.3401

Question 78

Use a calculator to evaluate the logarithm.

- $\ln 96$

A) 1.9823
B) 4.5643
C) 35.4244
D) 0.2184

Question 79

Use a calculator to evaluate the logarithm.

- $\ln 0.981$

A) 0.0192
B) -0.0083
C) 0.0083
D) -0.0192

Question 80

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers.

- $\log 64-\log 8$

A) $\log \frac{1}{8}$
B) $\log 16$
C) $\log 56$
D) $\log 8$