Deck 8: Exponential Functions and Logarithmic Functions

Question 1

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below)to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2001.

A)About $300,000
B)About $750,000
C)About $1,300,000
D)About $1,000,000

Answer 1

About $1,000,000

Question 2

Graph.

A)
B)
C)
D)

Answer 2

Question 3

Solve the problem.
Suppose that $50,000 is invested at 8% interest, compounded annually. Find a function A for the amount in the account after t years.

A)
B)
C)
D)

Answer 3

Question 4

Graph.

A)
B)
C)
D)

Question 5

Graph.

A)
B)
C)
D)

Question 6

Solve the problem.
The number of bacteria growing in an incubation culture increases with time according to where x is time in days. Find the number of bacteria when x = 0 and x = 4 .

A)3600 ; 28,800
B)3600 ; 14,400
C)3600 ; 57,600
D)7200 ; 57,600

Question 7

Solve the problem.
The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by D(x)= where x is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at x = 0 and x = 2 .

A)1500 ; 13,500
B)1500 ; 40,500
C)4500 ; 13,500
D)1500 ; 9000

Question 8

Graph.

A)
B)
C)
D)

Question 9

Graph.

A)
B)
C)
D)

Question 10

Graph.

A)
B)
C)
D)

Question 11

Graph.

A)
B)
C)
D)

Question 12

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below)to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year 2002.

A)About $500,000
B)About $800,000
C)About $900,000
D)About $1,000,000

Question 13

Solve the problem.
The half-life of Krypton 88 is 2.8 hours. If the formula gives the percent (as a decimal)remaining after time t (in hours), sketch P versus t.

A)
B)
C)
D)

Question 14

Solve the problem.
A computer is purchased for $4300. Its value each year is about 79% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function Find the value of the computer after 8 years.

A)$515.36
B)$27,176.00
C)$652.36
D)$407.14

Question 15

Graph.

A)
B)
C)
D)

Question 16

Solve the problem.
The amount of particulate matter left in solution during a filtering process decreases by the equation where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

A)800; 25
B)800; 3200
C)800; 200
D)1600 ; 200

Question 17

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below)to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2002.

A)About $1,300,000
B)About $1,000,000
C)About $1,700,000
D)About $750,000

Question 18

Solve the problem.
The half-life of a certain radioactive substance is 17 years. Suppose that at time t = 0, there are 30 g of the substance. Then after t years, the number of grams of the substance remaining will be: How many grams of the substance will remain after 136 years? Round to the nearest hundredth when necessary.

A)0.47 g
B)1.88 g
C)0.94 g
D)0.23 g

Question 19

Graph.

A)
B)
C)
D)

Question 20

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below)to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year 2001.

A)About $900,000
B)About $800,000
C)About $500,000
D)About $700,000

Question 21

Find the requested composition of functions.
Given and g(x)= x - 1, find g°f(x).

A)
B)
C)
D)

Question 22

Find the requested composition of functions.
Given , find f°g(x).

A)
B)
C)
D)

Question 23

Find the inverse of the relation.
{(4, 7), (-13, -8), (2, -11)}

A){(7, 4), (-8, -13), (-11, 2)}
B){(4, -8), (4, -13), (-11, 2)}
C){(7, 4), (2, -13), (-11, -8)}

Question 24

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 25

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 26

Find the requested composition of functions.
Given find g°f(x).

A)
B)x + 12
C)7x + 36
D)x

Question 27

Find the requested composition of functions.
Given find f°g(x).

A)
B)
C)
D)

Question 28

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 29

Find the requested composition of functions.
Given .

A)
B)
C)
D)

Question 30

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 31

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 32

Find the inverse of the relation.
{(6, 5), (11, 6), (9, 7), (7, 8)}

A){(6, 5), (8, 9), (6, 9), (6, 7)}
B){(5, 6), (6, 11), (7, 9), (8, 7)}
C){(6, 5), (5, 9), (6, 11), (6, 7)}

Question 33

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 34

Find the requested composition of functions.
Given f(x)= 5x + 12 and g(x)= 4x - 1, find f°g(x).

A)
B)
C)
D)

Question 35

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 36

Find the inverse of the relation.
{(9, 7), (-7, -9), (-1, -5), (1, 5)}

A){(5, -1), (-9, -7), (7, -7), (-5, 1)}
B){(7, 9), (-9, -7), (-5, -1), (5, 1)}
C){(5, -1), (-1, -7), (7, 9), (-5, 1)}

Question 37

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 38

Find the inverse of the relation.
{(-4, -3), (4, 3), (9, 5), (-9, -5)}

A){(-3, -4), (-4, 4), (5, 9), (-5, -9)}
B){(-3, -4), (3, 4), (5, 4), (-5, -9)}
C){(-3, -4), (3, 4), (5, 9), (-5, -9)}

Question 39

Find f(x)and g(x)such that h(x)=

A)
B)
C)
D)

Question 40

Find the requested composition of functions.
Given find g°f(x).

A)
B)
C)
D)

Question 41

Determine whether the function is one-to-one.

A)Yes
B)No

Question 42

Determine whether the function is one-to-one.

A)Yes
B)No

Question 43

Graph the relation using solid circles and the inverse using open circles.
{(-16, -4), (-14, -7), (18, 12)}

A)
B)
C)
D)

Question 44

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.

A)
B)
C)
D)

Question 45

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.

A)
B)
C)
D)

Question 46

Graph the relation using solid circles and the inverse using open circles.
{(2, 5), (-2, -5), (8, -3), (-8, 3)}

A)
B)
C)
D)

Question 47

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.

A)
B)
C)
D)

Question 48

Determine whether the function is one-to-one.

A)Yes
B)No

Question 49

Determine whether the function is one-to-one.

A)No
B)Yes

Question 50

Determine whether the function is one-to-one.

A)No
B)Yes

Question 51

Determine whether the function is one-to-one.

A)No
B)Yes

Question 52

Find an equation of the inverse of the relation.

A)
B)
C)
D)

Question 53

Graph the relation using solid circles and the inverse using open circles.
{(8, -6), (6, -5), (4, -4), (2, -3)}

A)
B)
C)
D)

Question 54

Find an equation of the inverse of the relation.

A)
B)
C)y = 8 + 6x
D)x = 8 + 6y

Question 55

Graph the relation using solid circles and the inverse using open circles.
{(-4, 9), (-9, 4), (-4, 5), (4, -5)}

A)
B)
C)
D)

Question 56

Determine whether the function is one-to-one.

A)No
B)Yes

Question 57

Find an equation of the inverse of the relation.

A)
B)
C)
D)

Question 58

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.

A)
B)
C)
D)

Question 59

Find an equation of the inverse of the relation.

A)
B)
C)
D)

Question 60

Determine whether the function is one-to-one.

A)Yes
B)No

Question 61

Graph the function as a solid curve and its inverse as a dashed curve.

A)
B)
C)
D)

Question 62

Determine whether the function is one-to-one.

A)Yes
B)No

Question 63

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

A)
B)
C)
D)Not a one-to-one function

Question 64

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

A)Not a one-to-one function
B)
C)
D)

Question 65

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

A)
B)
C)Not a one-to-one function
D)

Question 66

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

A)
B)
C)Not a one-to-one function
D)

Question 67

Graph the function as a solid curve and its inverse as a dashed curve.

A)
B)
C)
D)

Question 68

Graph the function as a solid curve and its inverse as a dashed curve.

A)
B)
C)
D)

Question 69

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

A)
B)
C)Not a one-to-one function
D)

Question 70

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

A)
B)
C)
D)Not a one-to-one function

Question 71

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

A)Not a one-to-one function
B)
C)
D)