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Algebra 2

Prentice Hall, Basia Kennedy, Dan Ramirez

Chapter 8

Exponential Logarithmic Functions

Educators

RL

Problem 1

Graph each function.
$$
y=6^{x}
$$

RL
Robert L.
Numerade Educator

Problem 2

Graph each function.
$$
y=3(10)^{x}
$$

Mariam S.
Numerade Educator

Problem 3

Graph each function.
$$
y=1000(2)^{x}
$$

RL
Robert L.
Numerade Educator

Problem 4

Graph each function.
$$
y=9(3)^{x}
$$

Mariam S.
Numerade Educator

Problem 5

Graph each function.
$$
f(x)=2(3)^{x}
$$

RL
Robert L.
Numerade Educator

Problem 6

Graph each function.
$$
s(t)=1.5^{t}
$$

Mariam S.
Numerade Educator

Problem 7

Graph each function.
$$
y=8(5)^{x}
$$

RL
Robert L.
Numerade Educator

Problem 8

Graph each function.
$$
y=2^{2 x}
$$

Mariam S.
Numerade Educator

Problem 9

Population The world population in 2000 was approximately 6.08 billion. The annual rate of increase was about 1.26$\% .$
a. Find the growth factor for the world population.
b. Suppose the rate of increase continues to be 1.26$\% .$ Write a function to model world population growth.

RL
Robert L.
Numerade Educator

Problem 10

Write an exponential function $y=a b^{x}$ for a graph that includes the given points.
$$
(4,8),(6,32)
$$

Mariam S.
Numerade Educator

Problem 11

Write an exponential function $y=a b^{x}$ for a graph that includes the given points.
$$
(2,122.5),(3,857.5)
$$

RL
Robert L.
Numerade Educator

Problem 12

Write an exponential function $y=a b^{x}$ for a graph that includes the given points.
$$
(2,18),(5,60.75)
$$

Mariam S.
Numerade Educator

Problem 13

Write an exponential function $y=a b^{x}$ for a graph that includes the given points.
$$
\left(-1,8 \frac{1}{3}\right),(2,1.8)
$$

RL
Robert L.
Numerade Educator

Problem 14

Write an exponential function $y=a b^{x}$ for a graph that includes the given points.
$$
(-3,24),(-2,12)
$$

Mariam S.
Numerade Educator

Problem 15

Write an exponential function $y=a b^{x}$ for a graph that includes the given points.
$$
(0,24),\left(3, \frac{8}{9}\right)
$$

RL
Robert L.
Numerade Educator

Problem 16

Without graphing, determine whether each function represents exponential growth or exponential decay.
$$
y=129(1.63)^{x}
$$

Mariam S.
Numerade Educator

Problem 17

Without graphing, determine whether each function represents exponential growth or exponential decay.
$$
f(x)=2(0.65)^{x}
$$

RL
Robert L.
Numerade Educator

Problem 18

Without graphing, determine whether each function represents exponential growth or exponential decay.
$$
y=12\left(\frac{17}{10}\right)^{x}
$$

Mariam S.
Numerade Educator

Problem 19

Without graphing, determine whether each function represents exponential growth or exponential decay.
$$
y=0.8\left(\frac{1}{8}\right)^{x}
$$

RL
Robert L.
Numerade Educator

Problem 20

Without graphing, determine whether each function represents exponential growth or exponential decay.
$$
f(x)=4\left(\frac{5}{6}\right)^{x}
$$

Mariam S.
Numerade Educator

Problem 21

Without graphing, determine whether each function represents exponential growth or exponential decay.
$$
y=0.45 \cdot 3^{x}
$$

RL
Robert L.
Numerade Educator

Problem 22

Without graphing, determine whether each function represents exponential growth or exponential decay.
$$
y=\frac{1}{100}\left(\frac{4}{3}\right)^{x}
$$

Mariam S.
Numerade Educator

Problem 23

Without graphing, determine whether each function represents exponential growth or exponential decay.
$$
f(x)=2^{-x}
$$

RL
Robert L.
Numerade Educator

Problem 24

Graph each function.
$$
y=(0.75)^{x}
$$

Mariam S.
Numerade Educator

Problem 25

Graph each function.
$$
y=2(0.5)^{x}
$$

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Problem 26

Graph each function.
$$
y=(0.25)^{x}
$$

Mariam S.
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Problem 27

Graph each function.
$$
g(x)=5(0.2)^{x}
$$

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Problem 28

Graph each function.
$$
f(x)=\left(\frac{1}{5}\right)^{x}
$$

Mariam S.
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Problem 29

Graph each function.
$$
y=81\left(\frac{1}{3}\right)^{x}
$$

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Problem 30

Graph each function.
$$
s(t)=\left(\frac{1}{10}\right)^{t}
$$

Mariam S.
Numerade Educator

Problem 31

Graph each function.
$$
y=\frac{1}{2}\left(\frac{1}{2}\right)^{x}
$$

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Problem 32

Write an exponential function for each graph. Evaluate the function for $x=6$
(GRAPH NOT COPY)

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Problem 33

Write an exponential function for each graph. Evaluate the function for $x=6$
(GRAPH NOT COPY)

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Problem 34

Write an exponential function for each graph. Evaluate the function for $x=6$
(GRAPH NOT COPY)

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Problem 35

Business A computer valued at $\$ 6500$ depreciates at the rate of 14.3$\%$ per year.
a. Write a function that models the value of the computer.
b. Find the value of the computer after three years.

RL
Robert L.
Numerade Educator

Problem 36

For each function, find the percent increase or decrease that the function models.
$$
y=1298(1.63)^{x}
$$

Mariam S.
Numerade Educator

Problem 37

For each function, find the percent increase or decrease that the function models.
$$
y=0.65(1.3)^{x}
$$

RL
Robert L.
Numerade Educator

Problem 38

For each function, find the percent increase or decrease that the function models.
$$
f(x)=2(0.65)^{x}
$$

Mariam S.
Numerade Educator

Problem 39

For each function, find the percent increase or decrease that the function models.
$$
y=12\left(\frac{17}{10}\right)^{x}
$$

RL
Robert L.
Numerade Educator

Problem 40

For each function, find the percent increase or decrease that the function models.
$$
y=0.8\left(\frac{1}{8}\right)^{x}
$$

Mariam S.
Numerade Educator

Problem 41

For each function, find the percent increase or decrease that the function models.
$$
y=16\left(\frac{1}{4}\right)^{x}
$$

RL
Robert L.
Numerade Educator

Problem 42

Multiple Choice According to the projected growth rate, how will these regions rank from largest to smallest populations in 2015 ?
(TABLE NOT COPY)
A. Tokyo, Mexico City, Sâo Paulo, Mumbai
B. Tokyo, Mexico City, Mumbai, Sâo Paulo
C. Tokyo, Mumbai, Säo Paulo, Mexico City
D. Tokyo, Säo Paulo, Mexico City, Mumbai

Mariam S.
Numerade Educator

Problem 43

Oceanography The function $y=20 \cdot 0.97^{x}$ models the intensity of sunlight beneath the surface of the ocean. The output $y$ represents the percent of surface sunlight intensity that reaches a depth of $x$ feet. The model is accurate from about 20 feet to about 600 feet beneath the surface.
a. Find the percent of sunlight 50 feet beneath the surface of the ocean.
b. Find the percent of sunlight at a depth of 370 $\mathrm{ft}$ .

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Problem 44

a. Depreciation Each graph below shows the expected decrease in a car's value over the next five years. Write a function to model each car's depreciation. Determine which car will be worth more after 10 years.
b. Data collection Find the initial value and the expected decrease in value of your favorite type of car. Write an exponential function to model the car's depreciation.

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Problem 45

The population of a certain animal species decreases at a rate of 3.5$\%$ pear. You have counted 80 of the animals in the habitat you are studying.
a. Write a function that models the change in the animal population.
b. Graph the function. Estimate the number of years until the population. drops below 15 animals.

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Problem 46

For each annual rate of change, find the corresponding growth or decay factor.
$$
+70 \%
$$

Mariam S.
Numerade Educator

Problem 47

For each annual rate of change, find the corresponding growth or decay factor.
$$
+500 \%
$$

RL
Robert L.
Numerade Educator

Problem 48

For each annual rate of change, find the corresponding growth or decay factor.
$$
-75 \%
$$

Mariam S.
Numerade Educator

Problem 49

For each annual rate of change, find the corresponding growth or decay factor.
$$
-55 \%
$$

RL
Robert L.
Numerade Educator

Problem 50

For each annual rate of change, find the corresponding growth or decay factor.
$$
+12.5 \%
$$

Mariam S.
Numerade Educator

Problem 51

For each annual rate of change, find the corresponding growth or decay factor.
$$
-0.1 \%
$$

RL
Robert L.
Numerade Educator

Problem 52

For each annual rate of change, find the corresponding growth or decay factor.
$$
+0.1 \%
$$

Mariam S.
Numerade Educator

Problem 53

For each annual rate of change, find the corresponding growth or decay factor.
$$
+100 \%
$$

RL
Robert L.
Numerade Educator

Problem 54

Communications Cellular phone usage grew about 22$\%$ each year from 1995 (about 34 million) to 2003 . Write a function to model U.S. cellular phone usage over that time period.

Mariam S.
Numerade Educator

Problem 55

Open-Ended Write a problem that could be modeled with $y=20(1.1)^{x} .$

RL
Robert L.
Numerade Educator

Problem 56

The value of an industrial machine has a decay factor of 0.75 per year. After six years, the machine is
worth $\$ 7500 .$ What was the original value of the machine?

Mariam S.
Numerade Educator

Problem 57

Zoology Determine which situation best matches the graph.
A. A population of 120 cougars decreases 98.75$\%$ yearly.
B. A population of 125 cougars increases 1.25$\%$ yearly.
C. A population of 115 cougars decreases 1.25$\%$ yearly.
D. A population of 200 cougars decreases 50$\%$ yearly.

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Problem 58

Critical Thinking Analyze the graph at the left to determine which function the graph represents. Explain your reasoning.
$$\begin{array}{llll}{\text { A. } y=\left(\frac{1}{3}\right) 2^{x}} & {\text { B. } y=2\left(\frac{1}{3}\right)^{x}} & {\text { C. } y=-2\left(\frac{1}{3}\right)^{x}}\end{array}$$

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Problem 59

Economics The table gives the 2003 gross domestic product and the real growth rate for several countries.
A. Writing Explain how a negative growth rate affects the equation for an exponential model.
b. Write a function for each country to model the GDP.
c. Suppose the given real growth rates continue. Predict the gross domestic product for each country in 2008 .

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Problem 60

Which function represents exponential growth?
$$\begin{array}{ll}{\text { A. } y=35 x \cdot 35} & {\text { B. } y=35 \cdot(0.35)^{x}} \\ {\text { C. } y=35 \cdot(1.35)^{x}} & {\text { D. } y=35 \div(1.35)^{x}}\end{array}$$

Mariam S.
Numerade Educator

Problem 61

Which function represents the value after $x$ years of a delivery van that was purchased new for $\$ 17,500$ and depreciates 11$\%$ each year?
F. $y=-11(17,500)^{x}$
H. $y=17,500(0.89)^{x}$
G. $y=17,500(0.11)^{x}$
J. $y=17,500(1.11)^{x}$

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Problem 62

What is the equation of the asymptote of $y=15 \cdot\left(\frac{1}{3}\right)^{x} ?$
$$\begin{array}{llll}{\text { A. } y=1} & {\text { B. } y=0} & {\text { C. } y=x} & {\text { D. } y=\frac{1}{3}}\end{array}$$

Mariam S.
Numerade Educator

Problem 63

Sketch the graph of the function $y=2 \cdot\left(\frac{1}{4}\right)^{x}$

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Problem 64

Write an exponential equation in the form $y=a b^{x}$ for a graph that includes $(2,54)$ and $\left(\frac{1}{2}, 2\right) .$ Show your work.

Mariam S.
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Problem 65

Graph each function.
$$
y=\sqrt{x+2}
$$

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Problem 66

Graph each function.
$$
y=-2 \sqrt[3]{x}+4
$$

Mariam S.
Numerade Educator

Problem 67

Graph each function.
$$
y=\sqrt{9 x-153}-5
$$

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Problem 68

Simplify each expression.
$$
\sqrt{180 n^{5}}
$$

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Problem 69

Simplify each expression.
$$
3 \sqrt[3]{72 r^{5}} \cdot 2 \sqrt[3]{343 r^{3}}
$$

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Problem 70

Simplify each expression.
$$
\frac{\sqrt{64 x^{4}}}{\sqrt{144 x^{5}}}
$$

Mariam S.
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Problem 71

Construct a polynomial function with the given zeros.
$$
x=0,1,4
$$

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Problem 72

Construct a polynomial function with the given zeros.
$$
x=-2,-1,3
$$

Mariam S.
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Problem 73

Construct a polynomial function with the given zeros.
$$
x=5,0,2
$$

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Problem 74

Each point lies on a parabola with vertex $(0,2) .$ Write the equation of the parabola.
$$
(1,3)
$$

Mariam S.
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Problem 75

Each point lies on a parabola with vertex $(0,2) .$ Write the equation of the parabola.
$$
(1,-3)
$$

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Problem 76

Each point lies on a parabola with vertex $(0,2) .$ Write the equation of the parabola.
$$
(-1,4)
$$

Mariam S.
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Problem 77

Each point lies on a parabola with vertex $(0,2) .$ Write the equation of the parabola.
$$
(2,42)
$$

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Problem 78

Each point lies on a parabola with vertex $(0,2) .$ Write the equation of the parabola.
$$
(-2,8)
$$

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Problem 79

Each point lies on a parabola with vertex $(0,2) .$ Write the equation of the parabola.
$$
(-1,5)
$$

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Problem 80

Each point lies on a parabola with vertex $(0,2) .$ Write the equation of the parabola.
$$
(2,0)
$$

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Problem 81

Each point lies on a parabola with vertex $(0,2) .$ Write the equation of the parabola.
$$
(2,-2)
$$

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