Deck 9: Exponential and Logarithmic Functions

Question 1

For the functions f ( x) = x + 9 and g( x) = 3x² + 7x , find:

-(f+g)(x)

Answer 1

Question 2

For the functions f ( x) = x + 9 and g( x) = 3x² + 7x , find:
-(f-g)(x)

Answer 2

Question 3

For the functions f ( x) = x + 9 and g( x) = 3x² + 7x , find:
- $(f\cdot{g})(x)$

Answer 3

Question 4

For the functions f ( x) = x + 9 and g( x) = 3x² + 7x , find:
-(f/g)(x)

Question 5

For the functions f ( x) = x + 9 and g( x) = 3x² + 7x , find:
- $(f\circ{g})(x)$

Question 6

For the functions f ( x) = x + 9 and g( x) = 3x² + 7x , find:
- $(g\circ{f})(x)$

Question 7

For the functions f(x) = x+12 and g(x) = 2 $\sqrt{x}$ , find:
-(g/f)(x)

Question 8

For the functions f(x) = x+12 and g(x) = 2 $\sqrt{x}$ , find:
-(g+f)(x)

Question 9

For the functions f(x) = x+12 and g(x) = 2 $\sqrt{x}$ , find:
-(g-f)(x)

Question 10

For the functions f(x) = x+12 and g(x) = 2 $\sqrt{x}$ , find:
-(f/g)(x)

Question 11

For the functions f(x) = x+12 and g(x) = 2 $\sqrt{x}$ , find:
- $(g\circ{f})(x)$

Question 12

For the functions f(x) = x+12 and g(x) = 2 $\sqrt{x}$ , find:
- $(g\circ{f})(4)$

Question 13

For the functions f ( x) = -8x + 7 and g( x) = x² + x - 5, find:
-( f + g)( x)

Question 14

For the functions f ( x) = -8x + 7 and g( x) = x² + x - 5, find:
-( f - g)( x)

Question 15

For the functions f ( x) = -8x + 7 and g( x) = x² + x - 5, find:
-( g - f )( x)

Question 16

For the functions f ( x) = -8x + 7 and g( x) = x² + x - 5, find:
-( g $\circ$ f )( x)

Question 17

For the functions f ( x) = -8x + 7 and g( x) = x² + x - 5, find:
-( f $\circ$ g)( x)

Question 18

For the functions f ( x) = -8x + 7 and g( x) = x² + x - 5, find:
-( g + f )(3)

Question 19

For the functions f ( x) = -8x + 7 and g( x) = x² + x - 5, find:
-(g/f)(x)

Question 20

For the functions f ( x) = -8x + 7 and g( x) = x² + x - 5, find:
-(f-g)(8)

Question 21

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function.
-f = {(0, 1), (9, 2), (8, 7), (1, 6)}

Question 22

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function.
-g = {(3, 2), (1, 7), (10, -2), (2, 3)}

Question 23

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function.
-h = {(7, 6), (3, 1), (-7, 2), (0, 1)}

Question 24

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function.
-r = {(0, -2), (-1, 7), (12, -2), (1, 0)}

Question 25

Determine whether the graph of each function is the graph of a one-to-one function.
-

Question 26

Determine whether the graph of each function is the graph of a one-to-one function.
-

Question 27

Determine whether the graph of each function is the graph of a one-to-one function.
-

Question 28

Determine whether the graph of each function is the graph of a one-to-one function.
-

Question 29

Determine whether the graph of each function is the graph of a one-to-one function.
-

Question 30

Determine whether the graph of each function is the graph of a one-to-one function.
-

Question 31

Each of the following functions is one-to-one. Find the inverse of each function.
-f ( x) = 3x + 4

Question 32

Each of the following functions is one-to-one. Find the inverse of each function.
-f ( x) = 3 - 2 x

Question 33

Each of the following functions is one-to-one. Find the inverse of each function.
-g( x) = 2x + 6

Question 34

Each of the following functions is one-to-one. Find the inverse of each function.
-g( x) = 4x - 8

Question 35

Each of the following functions is one-to-one. Find the inverse of each function.
-h( x) = x³ - 8

Question 36

Each of the following functions is one-to-one. Find the inverse of each function.
- $h(x) =\frac1x$

Question 37

Each of the following functions is one-to-one. Find the inverse of each function.
- $f(x) = \frac{2x+3}{x+4}$

Question 38

Each of the following functions is one-to-one. Find the inverse of each function.
- $f(x) = \frac{x-5}{2x+3}$

Question 39

Each of the following functions is one-to-one. Find the inverse of each function.
-Graph f(x) = 5x - 3 and its inverse on the same axes.

Question 40

Each of the following functions is one-to-one. Find the inverse of each function.
-Graph $f(x) = -\frac13x - 3$ and its inverse on the same axes.

Question 41

Graph each exponential function.
- $y=3^x$

Question 42

Graph each exponential function.
- $y=(1/3)^x$

Question 43

Graph each exponential function.
- $y=5^x$

Question 44

Graph each exponential function.
- $y=(3/4)^x$

Question 45

Graph each exponential function.
- $y=2+3^x$

Question 46

Graph each exponential function.
- $y=4^x-2$

Question 47

Graph each exponential function.
- $y=(1/2)^x-3$

Question 48

Graph each exponential function.
- $y=(3/4)^x+1$

Question 49

Graph each exponential function.
- $y=-4^x$

Question 50

Graph each exponential function.
- $y=-(1/6)^x$

Question 51

Solve
- $16^x=64$

Question 52

Solve
- $4^{x+1}=16$

Question 53

Solve
- $7^{-x}=1/7$

Question 54

Solve
- $16^x=32$

Question 55

Solve
- $(3/4)^x=9/16$

Question 56

Solve
- $32^x=1/8$

Question 57

Solve
- $5^{x-12}=25^{2x}$

Question 58

Solve
- $3^{x+1}=9^{x+5}$

Question 59

Solve
-The exponential function $f(x) = 5000(2)^{0.04x}$ is a model for the population of a community x years after 1990. Predict the population for 2006

Question 60

Solve
-Use $A=P(1+\frac{r}n)^{nt}$ to find the total investment if $10,000 is invested for one year at 12% compounded quarterly

Question 61

Use the exponential growth model to find the final amount after x years of exponential growth given the initial amount C, growth rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-C = 800, r = 0.06, x = 4

Question 62

Use the exponential growth model to find the final amount after x years of exponential growth given the initial amount C, growth rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-C = 6700, r = 0.09, x = 36

Question 63

Use the exponential growth model to find the final amount after x years of exponential growth given the initial amount C, growth rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-C = 43, r = 0.25, x = 22

Question 64

Use the exponential growth model to find the final amount after x years of exponential growth given the initial amount C, growth rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-Initial amount is 592, growth rate per year is 17%, and number of years is 52.

Question 65

Use the exponential growth model to find the final amount after x years of exponential growth given the initial amount C, growth rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-Initial amount is 3500, growth rate per year is 2%, and number of years is 75.

Question 66

Use the exponential growth model to find the final amount after x years of exponential growth given the initial amount C, growth rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-Initial amount is 45, growth rate per year is 30%, and number of years is 16

Question 67

Use the exponential decay model to find the final amount after x years of exponential decay given the initial amount C, decay rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-C = 800, r = 0.06, x = 4

Question 68

Use the exponential decay model to find the final amount after x years of exponential decay given the initial amount C, decay rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-C = 6700, r = 0.09, x = 36

Question 69

Use the exponential decay model to find the final amount after x years of exponential decay given the initial amount C, decay rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-C = 3000, r = 0.5, x = 8

Question 70

Use the exponential decay model to find the final amount after x years of exponential decay given the initial amount C, decay rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-Initial amount is 9200, decay rate per year is 13%, and number of years is 40.

Question 71

Use the exponential decay model to find the final amount after x years of exponential decay given the initial amount C, decay rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-Initial amount is 70,000, decay rate per year is 10%, and number of years is 18.

Question 72

Use the exponential decay model to find the final amount after x years of exponential decay given the initial amount C, decay rate per year r, and the number of years x. Round final amounts to the nearest whole number.
-Initial amount is 32,000, decay rate per year is 5%, and number of years is 84.

Question 73

Solve. Round answers to the nearest whole number.
-Suppose a city with population 200,000 has been growing at a rate of 2% per year. If this rate continues, find the population of the city in 16 years.

Question 74

Solve. Round answers to the nearest whole number.
-Suppose a city with population 450,000 has been shrinking at a rate of 1.5% per year. If this rate continues, find the population of the city in 30 years.

Question 75

Solve. Round answers to the nearest whole number.
-The number of consumers in a certain area who subscribe to residential telephone service has been decreasing each year by 12%. If there are currently 13,000 subscribers in this area, find the number of subscribers in 5 years.

Question 76

Solve. Round answers to the nearest whole number.
-At a certain college, the number of students who utilize career placement services is growing at a rate of 4% per year. If the number of students who currently use career placement services is 2800, find how many students should use these services in 8 years.

Question 77

Solve. Round answers to the nearest whole number.
-The size of the jackrabbit population in a prairie preserve area grows at a rate of 11% per year. If there are 132 jackrabbits currently, find how many jackrabbits there should be in 4 years.

Question 78

Solve. Round answers to the nearest whole number.
-The size of the cod population off the coast of New England declines at a rate of 8.5% per year. If the population is currently 400,000, find how many cod there should be in 12 years.

Question 79

Solve. Round answers to the nearest tenth.
-A form of sodium has a half-life of 2.6 years. How much of a 600-gram sample is left after 13 years?

Question 80

Solve. Round answers to the nearest tenth.
-A form of magnesium has a half-life of 21 hours. How much of a 900-gram sample is left after 252 hours?