# Algebra 2

## Educators

RL

Problem 1

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

RL
Robert L.

Problem 2

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

Mariam S.

Problem 3

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

RL
Robert L.

Problem 4

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

Mariam S.

Problem 5

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

RL
Robert L.

Problem 6

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

Mariam S.

Problem 7

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

RL
Robert L.

Problem 8

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

Mariam S.

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.

Problem 10

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

Mariam S.

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.

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.

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.

Problem 14

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

Mariam S.

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.

Problem 16

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

Mariam S.

Problem 17

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

RL
Robert L.

Problem 18

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

Mariam S.

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.

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.

Problem 21

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

RL
Robert L.

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.

Problem 23

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

RL
Robert L.

Problem 24

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

Mariam S.

Problem 25

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

Check back soon!

Problem 26

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

Mariam S.

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.

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.

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$\mathrm{ft}$. Check back soon! 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. Check back soon! 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. Check back soon! 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.

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.
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.$y=17,500(1.11)^{x}$Check back soon! 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$y=2 \cdot\left(\frac{1}{4}\right)^{x}$Check back soon! 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. Numerade Educator Problem 65 Graph each function. $$y=\sqrt{x+2}$$ Check back soon! Problem 66 Graph each function. $$y=-2 \sqrt[3]{x}+4$$ Mariam S. Numerade Educator Problem 67 Graph each function. $$y=\sqrt{9 x-153}-5$$ Check back soon! Problem 68 Simplify each expression. $$\sqrt{180 n^{5}}$$ Mariam S. Numerade Educator Problem 69 Simplify each expression. $$3 \sqrt[3]{72 r^{5}} \cdot 2 \sqrt[3]{343 r^{3}}$$ Check back soon! Problem 70 Simplify each expression. $$\frac{\sqrt{64 x^{4}}}{\sqrt{144 x^{5}}}$$ Mariam S. Numerade Educator Problem 71 Construct a polynomial function with the given zeros. $$x=0,1,4$$ Check back soon! Problem 72 Construct a polynomial function with the given zeros. $$x=-2,-1,3$$ Mariam S. Numerade Educator Problem 73 Construct a polynomial function with the given zeros. $$x=5,0,2$$ Check back soon! Problem 74 Each point lies on a parabola with vertex$(0,2) .$Write the equation of the parabola. $$(1,3)$$ Mariam S. Numerade Educator Problem 75 Each point lies on a parabola with vertex$(0,2) .$Write the equation of the parabola. $$(1,-3)$$ Check back soon! Problem 76 Each point lies on a parabola with vertex$(0,2) .$Write the equation of the parabola. $$(-1,4)$$ Mariam S. Numerade Educator Problem 77 Each point lies on a parabola with vertex$(0,2) .$Write the equation of the parabola. $$(2,42)$$ Check back soon! Problem 78 Each point lies on a parabola with vertex$(0,2) .$Write the equation of the parabola. $$(-2,8)$$ Mariam S. Numerade Educator Problem 79 Each point lies on a parabola with vertex$(0,2) .$Write the equation of the parabola. $$(-1,5)$$ Check back soon! Problem 80 Each point lies on a parabola with vertex$(0,2) .$Write the equation of the parabola. $$(2,0)$$ Mariam S. Numerade Educator Problem 81 Each point lies on a parabola with vertex$(0,2) .\$ Write the equation of the parabola.
$$(2,-2)$$