Deck 5: Exponential and Logarithmic Functions

Question 1

Graph the function.

- $f(x)=4^{(x-1)}-1$

A)
B)
C)
D)

Answer 1

Question 2

Graph the function.
$f(x)=3 e^{-x}$

A)


B)

C)

D)

Answer 2

D

Question 3

$f ( x ) = 2 \cdot 0.7 ^ { 4 x }$

A)
B)
C)
D)

Answer 3

D

Question 4

Determine whether or not the given function is an exponential function.
$y = e ^ { x ^ { 7 + 2 x } }$

A) exponential
B) not exponential

Question 5

Graph the function.

- $y=5(x-4)+2$

A)
B)
C)
D)

Question 6

Determine if the function is a growth exponential or a decay exponential.
$y = 3 ^ { 0.7 x }$

A) Growth
B) Decay

Question 7

Determine whether or not the given function is an exponential function.
$y = 4 ^ { x }$

A) exponential
B) not exponential

Question 8

Determine whether or not the given function is an exponential function.
$y = x ^ { 5 }$

A) exponential
B) not exponential

Question 9

Determine if the function is a growth exponential or a decay exponential.
$y = 9 e ^ { - 9 x }$

A) Growth
B) Decay

Question 10

Determine if the function is a growth exponential or a decay exponential.
$y = 0.2 ^ { 7 x }$

A) Growth
B) Decay

Question 11

Graph the function.
$f(x)=4^{-x}$

A)

B)


C)

D)

Question 12

Determine whether or not the given function is an exponential function.
y $= 3 x - 5$

A) exponential
B) not exponential

Question 13

Graph the function.
$f(x)=\left(\frac{1}{4}\right)^{x}$

A)

B)

C)

D)

Question 14

Graph the function.
$f(x)=2^{x}$

A)

B)
C)

D)

Question 15

Determine whether or not the given function is an exponential function.
$y = 6 x ^ { e }$

A) exponential
B) not exponential

Question 16

Graph the function.
$$f ( x ) = - 4 ^ { x }$$

A)

B)


C)


D)

Question 17

Determine whether or not the given function is an exponential function.
$y = x ^ { 7 } + 9 x$

A) exponential
B) not exponential

Question 18

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

A)
B)
C)
D)

Question 19

Determine if the function is a growth exponential or a decay exponential.
$y = 2 ^ { - 1.3 x }$

A) Growth
B) Decay

Question 20

Graph the function.
$f(x)=2(x-3)$

A)

B)

C)

D)

Question 21

Find the function value.
Let $f ( x ) = - 1.7 e ^ { - 0.8 x }$ . Find $f ( - 1.6 )$ , rounded to four decimal places.

A) $- 0.4727$
B) -6.1143
C) $0.4727$
D) $6.1143$

Question 22

Match the equation with its graph.
$$y = 4 ( x - 3 )$$

A)

B)

C)

D)

Question 23

In September 1998 the population of the country of West Goma in millions was modeled by $f ( x ) = 17.8 e ^ { 0.0015 x }$ . At the same time the population of East Goma in millions was modeled by $g ( x ) = 13.2 e ^ { 0.0164 x }$ . In both formulas $x$ is the year, where $x = 0$ corresponds to September 1998. Assuming these trends continue, estimate what the population will be when the populations are equal.

A) 18 million
B) 1 million
C) 16 million
D) 17 million

Question 24

In September 1998 the population of the country of West Goma in millions was modeled by $f ( x ) = 17.5 e ^ { 0.0010 x }$ . At the same time the population of East Goma in millions was modeled by $\mathrm { g } ( \mathrm { x } ) = 13.7 \mathrm { e } 0.0129 \mathrm { x }$ . In both formulas $x$ is the year, where $x = 0$ corresponds to September 1998 . Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma.

A) 21
B) 1977
C) 2019
D) 2016

Question 25

Match the equation with its graph.
$$y = \frac { 1 } { 3 } \cdot 3 ^ { x }$$

A)

B)

C)

D)

Question 26

Match the equation with its graph.
$$y = 4 ^ { x + 5 }$$

A)

B)

C)

D)

Question 27

Find the function value.
Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( - 2 )$ .

A) $\frac { 1 } { 36 }$
B) $- \frac { 1 } { 36 }$
C) 36
D) $- 12$

Question 28

Find the function value.
Let $f ( x ) = e ^ { 3 x }$ . Find $f ( - 0.50 )$ , rounded to four decimal places.

A) $- 0.2231$
B) $- 0.3502$
C) $0.3502$
D) $0.2231$

Question 29

Find the function value.
$\text { Let } f ( x ) = e ^ { - x } \text {. Find } f ( 3.9 ) \text {, rounded to four decimal places. }$

A) 1.4347
B) 10.6013
C) 49.4024
D) 0.0202

Question 30

The sales of a mature product (one which has passed its peak) will decline by the function $\left. \mathrm { S } ^ { \mathrm { t } } \right) = \mathrm { S } _ { 0 } \mathrm { e } ^ { - a t }$ , where $\mathrm { t }$ is time in years. Find the sales after 8 years if $\mathrm { a } = 0.18$ and $\mathrm { S } _ { 0 } = 48,500$ .

A) 58,065
B) 5746
C) 245,075
D) 11,491

Question 31

$y = 4 ( x + 4 ) + 1$

A)
B)
C)
D)

Question 32

Find the function value.
Let $f ( x ) = 3 ( 1 - x )$ . Find $f ( 3 )$ .

A) 9
B) $\frac { 1 } { 6 }$
C) $- 6$
D) $\frac { 1 } { 9 }$

Question 33

Match the equation with its graph.
$$y = 2 ^ { - x }$$

A)

B)

C)

D)

Question 34

$y = 2 \cdot 2 ^ { x }$

A)
B)
C)
D)

Question 35

Find the function value.
Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( 3 )$ .

A) 216
B) $\frac { 1 } { 216 }$
C) $\frac { 1 } { 729 }$
D) $\frac { 1 } { 18 }$

Question 36

Match the equation with its graph.
$$y = 2 ^ { x + 2 }$$

A)

B)

C)

D)

Question 37

The growth in the population of a certain rodent at a dump site fits the exponential function $A ( t ) = 102 e ^ { 0.018 t }$ where t is the number of years since 1965. Estimate the population in the year 2000.

A) 96
B) 195
C) 104
D) 192

Question 38

Find the function value.
$\text { Let } f ( x ) = 3 ^ { x } \text {. Find } f ( 2 )$

A) 27
B) 8
C) 9
D) 6

Question 39

Match the equation with its graph.
$$y = - 3 ^ { x }$$

A)

B)

C)

D)

Question 40

Find the function value.
Let $f ( x ) = 5 ^ { x }$ . Find $f ( - 2 )$ .

A) $\frac { 1 } { 32 }$
B) $- \frac { 1 } { 10 }$
C) $\frac { 1 } { 25 }$
D) $- 10$

Question 41

Give a definition for the following term: Exponential function .

Question 42

Provide an appropriate response.
What are the domain and range for the equation $y = 2 ^ { x }$ ?

A) Domain: $( \infty , \infty )$ ; range: $( \infty , \infty )$
B) Domain: $( 0 , \infty )$ ; range: $( \infty , \infty )$
C) Domain: $( \infty , \infty )$ ; range: $( 0 , \infty )$
D) $( \infty , \infty )$ ; range: $[ 0 , \infty )$

Question 43

The population of a small country increases according to the function $\mathrm { B } = 2,500,000 \mathrm { e } ^ { 0.02 \mathrm { t } }$ where t is measured in years. How many people will the country have after 3 years?

A) 3,054,622
B) 7,033,527
C) 2,870,384
D) 2,654,591

Question 44

Explain how the graph of $y = 4 ^ { x - 3 } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }$ .

Question 45

Explain how the graph of $y = - 4 \cdot 3 ^ { x } \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

Question 46

Provide an appropriate response.
Explain why f(x) $f ( x ) = 2 ^ { x } \text { is an exponential function but } f ( x ) = x ^ { 2 }$ is not.

Question 47

Write the logarithmic equation in exponential form.
$$\log _ { 3 } 9 = 2$$

A) $3 ^ { 2 } = 9$
B) $9 ^ { 2 } = 3$
C) $3 ^ { 9 } = 2$
D) $2 ^ { 3 } = 9$

Question 48

A computer is purchased for $4100. Its value each year is about 75% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function $\mathrm { V } ( \mathrm { t } ) = 4100 ( 0.75 ) ^ { \mathrm { t } }$ Find the value of the computer after
2 years.

A) $1297.27
B) $1729.69
C) $2306.25
D) $6150.00

Question 49

The number of acres in a landfill is given by the function $B = 2900 \mathrm { e } ^ { - 0.05 t }$ where t is measured in years. How many acres will the landfill have after 8 years? (Round to the nearest acre.)

A) 2657 acres
B) 1944 acres
C) 1154 acres
D) 1155 acres

Question 50

Provide an appropriate response.
Why can' $y = 2 ^ { x } \text { have an } x \text {-intercept }$

Question 51

Provide an appropriate response.
Why is an exponential function one-to-one?

Question 52

What is the range of the function $y = \left( \frac { 1 } { 5 } \right) ^ { x }$ ?

A) $( \infty , 0 )$
B) $( \infty , \infty )$
C) $( 0 , \infty )$
D) $[ 0 , \infty )$

Question 53

The amount of a certain radioactive isotope present at time t is given by $\mathrm { A } ( \mathrm { t } ) = 400 \mathrm { e } ^ { - 0.02664 \mathrm { t } }$ grams, where t is the time in years that the isotope decays. The initial amount present is 400 grams. How many grams remain
After 20 years? Round to the nearest hundredth.

A) 681.48 g
B) 234.78 g
C) 379.25 g
D) 397.87 g

Question 54

Provide an appropriate response.
With the exponential function f(x) $f ( x ) = a ^ { x } , \text { why must } a \neq 1$

Question 55

Write the logarithmic equation in exponential form.
$\log _ { 14 } 1 = 0$

A) $14 ^ { 1 } = 0$
B) $1 ^ { 14 } = 0$
C) $0 ^ { 14 } = 1$
D) $14 ^ { 0 } = 1$

Question 56

The half-life of Titanium 45 is $3.1$ hours. If the formula $\mathrm { P } ( \mathrm { t } ) = \left( \frac { 1 } { 2 } \right) ^ { \mathrm { t } / 3.1 }$ gives the percent (as a decimal) remaining after time $t$ (in hours), sketch $P$ versus t.

A)

B)

C)

D)

Question 57

Explain how the graph of $$y = - 5 \left( \frac { 1 } { 2 } \right) ^ { x } \text { can be obtained from the graph of } y = 2 ^ { x }$$

Question 58

The number of books in a small library increases according to the function B = 2700e0.05t, where t is measured in years. How many books will the library have after 4 years?

A) 3298 books
B) 4279 books
C) 4345 books
D) 1887 books

Question 59

Provide an appropriate response.
What is one ordered pair that is always on the graph of f( $f ( x ) = a ^ { x }$ ?

Question 60

What is the domain of the function $y = \left( \frac { 1 } { 8 } \right) ^ { x }$ ?

A) $$( -\infty , \infty )$$

B) $( 0 , \infty )$
C) $( \infty , 0 )$
D) $[ 0 , \infty )$

Question 61

Write in logarithmic form.
$$p = 9 ^ { t }$$

A) $\log _ { t } 9 = \mathrm { p }$
B) $\log _ { p } 9 = t$
C) $\log { 9 } \mathrm { p } = \mathrm { t }$
D) $\log _ { 9 } t = p$

Question 62

Evaluate the logarithm, if possible. Round the answer to four decimal places.
ln 0.000873 A) $3.0590$
B) $- 7.0436$
C) $- 3.0590$
D) $7.0436$

Question 63

Write the logarithmic equation in exponential form.
$\ln x = - 7$

A) $x = e ^ { 7 }$
B) No solution
C) $x = \ln - 7$
D) $x = e ^ { - 7 }$

Question 64

Evaluate the logarithm, if possible. Round the answer to four decimal places.
log 2.81

A) 0.4487
B) 0.4639
C) 1.0332
D) 0.4330

Question 65

$2 y = \ln ( - 8 x )$

A) $e ^ { - 8 x } = 2 y$
B) $- 8 x ^ { 2 } y = e$
C) $e ^ { y } = - 4 x$
D) $e ^ { 2 y } = - 8 x$

Question 66

Write the logarithmic equation in exponential form.
$$\log _ { 2 } ( 8 ) = 3$$

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

Question 67

$y = \log ( 2 x )$

A) $y ^ { 10 } = 2 x$
B) $10 y = 2 x$
C) $2 x y = 10$
D) $10 ^ { 2 x } = y$

Question 68

Write the logarithmic equation in exponential form.
$\log _ { W } Q = 19$

A) $w ^ { 19 } = \mathrm { Q }$
B) $19 \mathrm {~W} = \mathrm { Q }$
C) $\mathrm { Q } ^ { \mathrm { W } } = 19$
D) $Q ^ { 19 } = w$

Question 69

Evaluate the logarithm, if possible. Round the answer to four decimal places.
log 169

A) 5.1299
B) 2.2279
C) 2.2253
D) 2.2304

Question 70

Evaluate the logarithm, if possible. Round the answer to four decimal places.
ln 5,500,000

A) 4.0073
B) 15.5203
C) 6.7404
D) 0.0642

Question 71

Evaluate the logarithm, if possible. Round the answer to four decimal places.
ln 0.994

A) 0.0060
B) 0.0026
C) -0.0026
D) -0.0060

Question 72

Write in logarithmic form.
$$10 ^ { 3 } = 1000$$

A) $\log _ { 3 } 10 = 1000$
B) $\log _ { 3 } 1000 = 10$
C) $\log _ { 10 } 3 = 1000$
D) $\log _ { 10 } 1000 = 3$

Question 73

Write in logarithmic form.
$$4 ^ { 2 } = 16$$

A) $\log _ { 4 } 2 = 16$
B) $\log _ { 2 } 16 = 4$
C) $\log _ { 4 } 16 = 2$
D) $\log _ { 16 } 4 = 2$

Question 74

Write in logarithmic form.
$$6 ^ { 3 } = 216$$

A) $\log _ { 3 } 216 = 6$
B) $\log _ { 6 } 3 = 216$
C) $\log _ { 216 } 6 = 3$
D) $\log _ { 6 } 216 = 3$

Question 75

Evaluate the logarithm, if possible. Round the answer to four decimal places.
log 4508

A) 3.6549
B) 3.6530
C) 3.6540
D) 8.4136

Question 76

Write the logarithmic equation in exponential form.
$\log _ { 10 } 0 = - 10$

A) $- 10 ^ { 10 } = 0$
B) $0 ^ { - 10 } = 10$
C) $10 ^ { - 10 } = 0$
D) $0 ^ { 10 } = - 10$

Question 77

Evaluate the logarithm, if possible. Round the answer to four decimal places.
log 0.0743

A) $- 1.1349$
В) $- 1.1232$
C) $- 1.1290$
D) $- 2.5996$

Question 78

Write in logarithmic form.
$10 ^ { - 5 } = 0.00001$

A) $\log _ { 5 } .10 = - 5$
B) $\log _ { 10 } 0.00001 = - 5$
C) $\log _ { 10 } - 5 = 0.00001$
D) $\log _ { 5 } - 5 = .10$

Question 79

Evaluate the logarithm, if possible. Round the answer to four decimal places.
log 0.00474

A) $- 5.3517$
B) $- 2.3242$
C) $- 2.3152$
D) $- 2.3335$

Question 80

Write in logarithmic form.
$$9 ^ { 7 x } = y$$

A) $\log _ { 9 } 7 x = y$
B) $\log _ { y } 7 x = 9$
C) $\log _ { 9 } y = 7 x$
D) $\log _ { y } 9 = 7 x$