Introductory and Intermediate Algebra for College Students

Robert Blitzer

Chapter 9

Exponential and Logarithmic Functions - all with Video Answers

Educators

Section 1

Exponential Functions

Problem 1

Approximate each number using a calculator. Round your answer to three decimal places.
$$2^{3.4}$$

Pammi Eswari

Pammi Eswari

Numerade Educator

Problem 2

Approximate each number using a calculator. Round your answer to three decimal places.
$$3^{2.4}$$

Pammi Eswari

Numerade Educator

Problem 3

Approximate each number using a calculator. Round your answer to three decimal places.
$$3^{\sqrt{5}}$$

Ryan Mcalister

Numerade Educator

Problem 4

Approximate each number using a calculator. Round your answer to three decimal places.
$$5^{\sqrt{3}}$$

Ryan Mcalister

Numerade Educator

Problem 5

Approximate each number using a calculator. Round your answer to three decimal places.
$$4^{-1.5}$$

Pammi Eswari

Numerade Educator

Problem 6

Approximate each number using a calculator. Round your answer to three decimal places.
$$6^{-1.2}$$

Erika Bustos

Numerade Educator

Problem 7

Approximate each number using a calculator. Round your answer to three decimal places.
$$e^{2.3}$$

Ryan Mcalister

Numerade Educator

Problem 8

Approximate each number using a calculator. Round your answer to three decimal places.
$$e^{3.4}$$

Ryan Mcalister

Numerade Educator

Problem 9

Approximate each number using a calculator. Round your answer to three decimal places.
$$e^{-0.95}$$

Ryan Mcalister

Numerade Educator

Problem 10

Approximate each number using a calculator. Round your answer to three decimal places.
$$e^{-0.75}$$

Pammi Eswari

Numerade Educator

Problem 11

Set up a table of coordinates for each function. Select integers from -2 to $2,$ inclusive, for $x .$ Then use the table of coordinates to match the function with its graph. [The graphs are labeled $(a) \text { through }(f) .]$
$$f(x)=3^{x}$$

Brandon Fox

Numerade Educator

Problem 12

Set up a table of coordinates for each function. Select integers from -2 to $2,$ inclusive, for $x .$ Then use the table of coordinates to match the function with its graph. [The graphs are labeled $(a) \text { through }(f) .]$
$$f(x)=3^{x-1}$$

Brandon Fox

Numerade Educator

Problem 13

Set up a table of coordinates for each function. Select integers from -2 to $2,$ inclusive, for $x .$ Then use the table of coordinates to match the function with its graph. [The graphs are labeled $(a) \text { through }(f) .]$
$$f(x)=3^{x}-1$$

Brandon Fox

Numerade Educator

Problem 14

Set up a table of coordinates for each function. Select integers from -2 to $2,$ inclusive, for $x .$ Then use the table of coordinates to match the function with its graph. [The graphs are labeled $(a) \text { through }(f) .]$
$$f(x)=-3^{x}$$

Brandon Fox

Numerade Educator

Problem 15

Set up a table of coordinates for each function. Select integers from -2 to $2,$ inclusive, for $x .$ Then use the table of coordinates to match the function with its graph. [The graphs are labeled $(a) \text { through }(f) .]$
$$f(x)=3^{-x}$$

Brandon Fox

Numerade Educator

Problem 16

Set up a table of coordinates for each function. Select integers from -2 to $2,$ inclusive, for $x .$ Then use the table of coordinates to match the function with its graph. [The graphs are labeled $(a) \text { through }(f) .]$
$$f(x)=-3^{-x}$$

Brandon Fox

Numerade Educator

Problem 17

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
$$f(x)=4^{x}$$

Pammi Eswari

Numerade Educator

Problem 18

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
$$f(x)=5^{x}$$

Pammi Eswari

Numerade Educator

Problem 19

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
$$g(x)=\left(\frac{3}{2}\right)^{x}$$

Pammi Eswari

Numerade Educator

Problem 20

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
$$g(x)=\left(\frac{4}{3}\right)^{x}$$

Nick Johnson

Numerade Educator

Problem 21

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
$$h(x)=\left(\frac{1}{2}\right)^{x}$$

Nick Johnson

Numerade Educator

Problem 22

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
$$h(x)=\left(\frac{1}{3}\right)^{x}$$

Nick Johnson

Numerade Educator

Problem 23

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
$$f(x)=(0.6)^{x}$$

Nick Johnson

Numerade Educator

Problem 24

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
$$f(x)=(0.8)^{x}$$

Nick Johnson

Numerade Educator

Problem 25

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \text { and } g(x)=2^{x+1}$$

Ryan Mcalister

Numerade Educator

Problem 26

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \text { and } g(x)=2^{x+2}$$

Ryan Mcalister

Numerade Educator

Problem 27

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x-2}$$

Ryan Mcalister

Numerade Educator

Problem 28

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x-1}$$

Ryan Mcalister

Numerade Educator

Problem 29

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x}+1$$

Ryan Mcalister

Numerade Educator

Problem 30

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x}+2$$

Ryan Mcalister

Numerade Educator

Problem 31

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x}-2$$

Ryan Mcalister

Numerade Educator

Problem 32

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x}-1$$

Ryan Mcalister

Numerade Educator

Problem 33

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=3^{x} \text { and } g(x)=-3^{x}$$

Ryan Mcalister

Numerade Educator

Problem 34

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=3^{x} \quad \text { and } \quad g(x)=3^{-x}$$

Ryan Mcalister

Numerade Educator

Problem 35

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \text { and } g(x)=2^{x+1}-1$$

Ryan Mcalister

Numerade Educator

Problem 36

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x+1}-2$$

Ryan Mcalister

Numerade Educator

Problem 37

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=3^{x} \quad \text { and } \quad g(x)=\frac{1}{3} \cdot 3^{x}$$

Ryan Mcalister

Numerade Educator

Problem 38

Graph functions $f$ and g in the same rectangular coordinate system. Select integers from-2 to $2,$ inclusive, for $x .$ Then describe how the graph of g is related to the graph of f. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$f(x)=3^{x} \quad \text { and } \quad g(x)=3 \cdot 3^{x}$$

Ryan Mcalister

Numerade Educator

Problem 39

Use the compound interest formulas, $A=P\left(1+\frac{r}{n}\right)^{n t}$ and $A=P e^{r t},$ to solve Exercises. Round answers to the nearest cent.
Find the accumulated value of an investment of $\$ 10,000$ for 5 years at an interest rate of $5.5 \%$ if the money is
a. compounded semiannually;
b. compounded monthly;
c. compounded continuously.

Danielle Fairburn

Danielle Fairburn

Numerade Educator

Problem 40

Use the compound interest formulas, $A=P\left(1+\frac{r}{n}\right)^{n t}$ and $A=P e^{r t},$ to solve Exercises. Round answers to the nearest cent.
Find the accumulated value of an investment of $\$ 5000$ for 10 years at an interest rate of $6.5 \%$ if the money is
a. compounded semiannually;
b. compounded monthly;
c. compounded continuously.

Ryan Mcalister

Numerade Educator

Problem 41

Use the compound interest formulas, $A=P\left(1+\frac{r}{n}\right)^{n t}$ and $A=P e^{r t},$ to solve Exercises. Round answers to the nearest cent.
Suppose that you have $\$ 12,000$ to invest. Which investment yields the greater return over 3 years: $7 \%$ compounded monthly or $6.85 \%$ compounded continuously?

Ryan Mcalister

Numerade Educator

Problem 42

Suppose that you have $\$ 12,000$ to invest. Which investment yields the greater return over 3 years: $7 \%$ compounded monthly or $6.85 \%$ compounded continuously?Suppose that you have $\$ 6000$ to invest. Which investment yields the greater return over 4 years: $8.25 \%$ compounded quarterly or $8.3 \%$ compounded semiannually?

Ryan Mcalister

Numerade Educator

Problem 43

Use each exponential function's graph to determine the function's domain and range.

Ryan Mcalister

Numerade Educator

Problem 44

Use each exponential function's graph to determine the function's domain and range.

Ryan Mcalister

Numerade Educator

Problem 45

Use each exponential function's graph to determine the function's domain and range.

Ryan Mcalister

Numerade Educator

Problem 46

Use each exponential function's graph to determine the function's domain and range.

Ryan Mcalister

Numerade Educator

Problem 47

Use each exponential function's graph to determine the function's domain and range.

Ryan Mcalister

Numerade Educator

Problem 48

Use each exponential function's graph to determine the function's domain and range.

Ryan Mcalister

Numerade Educator

Problem 49

Graph $f$ and $g$ in the same rectangular coordinate system. Then find the point of intersection of the two graphs.
$$f(x)=2^{x}, g(x)=2^{-x}$$

Ryan Mcalister

Numerade Educator

Problem 50

Graph $f$ and $g$ in the same rectangular coordinate system. Then find the point of intersection of the two graphs.
$$f(x)=2^{x+1}, g(x)=2^{-x+1}$$

Ryan Mcalister

Numerade Educator

Problem 51

Graph $y=2^{x}$ and $x=2^{y}$ in the same rectangular coordinate system.

Nick Johnson

Numerade Educator

Problem 52

Graph $y=3^{x}$ and $x=3^{y}$ in the same rectangular coordinate system.

Nick Johnson

Numerade Educator

Problem 53

Use a calculator with a $\left[y^{x}\right]$ key or a [ ^ ] key to solve.
India is currently one of the world's fastest-growing countries. By $2040,$ the population of India will be larger than the population of China; by $2050,$ nearly one-third of the world's population will live in these two countries alone. The exponential function $f(x)=574(1.026)^{x}$ models the population of India, $f(x)$, in millions, $x$ years after 1974.
a. Substitute 0 for $x$ and, without using a calculator, find India's population in 1974
b. Substitute 27 for $x$ and use your calculator to find India's population, to the nearest million, in the year 2001 as modeled by this function.
c. Find India's population, to the nearest million, in the year 2028 as predicted by this function.
d. Find India's population, to the nearest million, in the year 2055 as predicted by this function.
e. What appears to be happening to India's population every 27 years?

Ryan Mcalister

Numerade Educator

Problem 54

Use a calculator with a $\left[y^{x}\right]$ key or a [ ^ ] key to solve.
The 1986 explosion at the Chernobyl nuclear power plant in the former Soviet Union sent about 1000 kilograms of radioactive cesium-137 into the atmosphere. The function $f(x)=1000(0.5)^{\frac{x}{30}}$ describes the amount, $f(x)$, in kilograms, of cesium-137 remaining in Chernobyl $x$ years after 1986 . If even 100 kilograms of cesium- 137 remain in Chernobyl's atmosphere, the area is considered unsafe for human habitation. Find $f(80)$ and determine if Chernobyl will be safe for human habitation by 2066.

Ryan Mcalister

Numerade Educator

Problem 55

The formula $S=C(1+r)^{t}$ models inflation, where $C=t h e$ value today, $r=$ the annual inflation rate, and $S=$ the inflated value t years from now. Round answers to the nearest dollar.
If the inflation rate is $6 \%,$ how much will a house now worth $\$ 465,000$ be worth in 10 years?

Ryan Mcalister

Numerade Educator

Problem 56

The formula $S=C(1+r)^{t}$ models inflation, where $C=t h e$ value today, $r=$ the annual inflation rate, and $S=$ the inflated value t years from now. Round answers to the nearest dollar.
If the inflation rate is $3 \%,$ how much will a house now worth $\$ 510,000$ be worth in 5 years?

Ryan Mcalister

Numerade Educator

Problem 57

Use a calculator with an $\left[e^{x}\right]$ key to solve. As of July 2010,500 million people worldwide shared versions of their lives on Facebook. The graph shows the number of active Facebook users (users who returned to the site within 30 days ) for selected months from 2009 through 2010 .
The data can be modeled by $$f(x)=19 x+127 \text { and } g(x)=152.6 e^{0.0667 x}$$
in which $f(x)$ and $g(x)$ represent the number of active Facebook users, in millions, $x$ months after December 2008 . Use these functions to solve Exercises $57-58$. Round answers to the nearest whole million.
a. According to the linear model, how many millions of active Facebook users were there in February 2010 , 14 months after December $2008 ?$
b. According to the exponential model, how many millions of active Facebook users were there in February 2010?
c. Which function is a better model for the data in February 2010?

Ryan Mcalister

Numerade Educator

Problem 58

Use a calculator with an $\left[e^{x}\right]$ key to solve. As of July 2010,500 million people worldwide shared versions of their lives on Facebook. The graph shows the number of active Facebook users (users who returned to the site within 30 days ) for selected months from 2009 through 2010 .
The data can be modeled by $$f(x)=19 x+127 \text { and } g(x)=152.6 e^{0.0667 x}$$
in which $f(x)$ and $g(x)$ represent the number of active Facebook users, in millions, $x$ months after December 2008 . Use these functions to solve Exercises $57-58$. Round answers to the nearest whole million.
a. According to the linear model, how many millions of active Facebook users were there in July 2010 , 19 months after December $2008 ?$
b. According to the exponential model, how many millions of active Facebook users were there in July $2010 ?$
c. Which function is a better model for the data in July $2010 ?$

Ryan Mcalister

Numerade Educator

Problem 59

In college, we study large volumes of information-information that, unfortunately, we do not often retain for very long. The function $$f(x)=80 e^{-0.5 x}+20$$ describes the percentage of information, $f(x),$ that a particular person remembers $x$ weeks after learning the information.
a. Substitute 0 for $x$ and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b. Substitute 1 for $x$ and find the percentage of information that is remembered after 1 week.
c. Find the percentage of information that is remembered after 4 weeks.
d. Find the percentage of information that is remembered after one year $(52$ weeks).

Ryan Mcalister

Numerade Educator

Problem 60

In $1626,$ Peter Minuit persuaded the Wappinger Indians to sell him Manhattan Island for $\$ 24 .$ If the Native Americans had put the $\$ 24$ into a bank account paying $5 \%$ interest, how much would the investment have been worth in the year 2005 if interest were compounded
a. monthly?
b. continuously?

Ryan Mcalister

Numerade Educator

Problem 61

The function $$f(x)=\frac{90}{1+270 e^{-0.122 x}}$$ models the percentage, $f(x)$, of people $x$ years old with some coronary heart disease. Use this function to solve . Round answers to the nearest tenth of a percent.
Evaluate $f(30)$ and describe what this means in practical terms.

Ryan Mcalister

Numerade Educator

Problem 62

The function $$f(x)=\frac{90}{1+270 e^{-0.122 x}}$$ models the percentage, $f(x)$, of people $x$ years old with some coronary heart disease. Use this function to solve . Round answers to the nearest tenth of a percent.
Evaluate $f(70)$ and describe what this means in practical terms.

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 63

The function $$N(t)=\frac{30,000}{1+20 e^{-1.5 t}}$$ describes the number of people, $N(t),$ who become ill with influenza $t$ weeks after its initial outbreak in a town with 30,000 inhabitants. The horizontal asymptote in the graph indicates that there is a limit to the epidemic's growth.
a. How many people became ill with the flu when the epidemic began? (When the epidemic began, $t=0 .)$
b. How many people were ill by the end of the third week?
c. Why can't the spread of an epidemic simply grow indefinitely? What does the horizontal asymptote shown in the graph indicate about the limiting size of the population that becomes ill?

Ryan Mcalister

Numerade Educator

Problem 64

What is an exponential function?

Narayan Hari

Numerade Educator

Problem 65

What is the natural exponential function?

Ryan Mcalister

Numerade Educator

Problem 66

Use a calculator to obtain an approximate value for $e$ to as many decimal places as the display permits. Then use the calculator to evaluate $\left(1+\frac{1}{x}\right)^{x}$ for $x=10,100,1000$ $10,000,100,000,$ and $1,000,000 .$ Describe what happens to the expression as $x$ increases.

Ryan Mcalister

Numerade Educator

Problem 67

Write an example similar to Example 7 on page 670 in which continuous compounding at a slightly lower yearly interest rate is a better investment than compounding $n$ times per year.

Ryan Mcalister

Numerade Educator

Problem 68

Describe how you could use the graph of $f(x)=2^{x}$ to obtain a decimal approximation for $\sqrt{2}$.

Ryan Mcalister

Numerade Educator

Problem 69

You have $\$ 10,000$ to invest. One bank pays $5 \%$ interest compounded quarterly and the other pays $4.5 \%$ interest compounded monthly.
a. Use the formula for compound interest to write a function for the balance in each account at any time $t$ in
years.
b. Use a graphing utility to graph both functions in an appropriate viewing rectangle. Based on the graphs, which bank offers the better return on your money?

Ryan Mcalister

Numerade Educator

Problem 70

a. Graph $y=e^{x}$ and $y=1+x+\frac{x}{2}$ in the same viewing rectangle.
b. Graph $y=e^{x}$ and $y=1+x+\frac{x^{2}}{2}+\frac{x^{3}}{6}$ in the same viewing rectangle.
c. Graph $y=e^{x}$ and $y=1+x+\frac{x^{2}}{2}+\frac{x^{3}}{6}+\frac{x^{4}}{24}$ in the
same viewing rectangle.
d. Describe what you observe in parts
(a)-(c). Try generalizing this observation.

Ryan Mcalister

Numerade Educator

Problem 71

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
My graph of $f(x)=3 \cdot 2^{x}$ shows that the horizontal asymptote for $f$ is $x=3$

Nick Johnson

Numerade Educator

Problem 72

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
I'm using a photocopier to reduce an image over and over by $50 \%,$ so the exponential function $f(x)=\left(\frac{1}{2}\right)^{x}$ models the new image size, where $x$ is the number of reductions.

Nick Johnson

Numerade Educator

Problem 73

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
Taxing thoughts: I'm looking at data that show the number of pages in the publication that explains the U.S. tax code for selected years from 1945 through 2009 . A linear function appears to be a better choice than an exponential function for modeling the number of pages in the tax code during this period.

Alison Rodriguez

Alison Rodriguez

Numerade Educator

Problem 74

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
I use the natural base $e$ when determining how much money I'd have in a bank account that earns compound interest subject to continuous compounding.

Nick Johnson

Numerade Educator

Problem 75

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
As the number of compounding periods increases on a fixed investment, the amount of money in the account over a fixed interval of time will increase without bound.

Nick Johnson

Numerade Educator

Problem 76

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
The functions $f(x)=3^{-x}$ and $g(x)=-3^{x}$ have the same graph.

Nick Johnson

Numerade Educator

Problem 77

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
If $f(x)=2^{x},$ then $f(a+b)=f(a)+f(b)$.

Nick Johnson

Numerade Educator

Problem 78

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
The functions $f(x)=\left(\frac{1}{3}\right)^{x}$ and $g(x)=3^{-x}$ have the same graph.

Ryan Mcalister

Numerade Educator

Problem 79

The graphs labeled (a)-(d) in the figure represent $y=3^{x}$, $y=5^{x}, y=\left(\frac{1}{3}\right)^{x},$ and $y=\left(\frac{1}{5}\right)^{x},$ but not necessarily in that order. Which is which? Describe the process that enables you to make this decision.

Ryan Mcalister

Numerade Educator

Problem 80

The hyperbolic cosine and hyperbolic sine functions are defined by \[\cosh x=\frac{e^{x}+e^{-x}}{2} \text { and } \sinh x=\frac{e^{x}-e^{-x}}{2} \] Prove that $(\cosh x)^{2}-(\sinh x)^{2}=1$.

Ryan Mcalister

Numerade Educator

Problem 81

Solve for
b: $\quad D=\frac{a b}{a+b}$
(Section 6.7, Example 1)

Ryan Mcalister

Numerade Educator

Problem 82

Evaluate: $\left|\begin{array}{ll}3 & -2 \\ 7 & -5\end{array}\right|$
(Section $3.5, \text { Example } 1)$

AG

Ankit Gupta

Numerade Educator

Problem 83

Solve: $\quad x(x-3)=10$
(Section 5.7, Example 2)

Kristen Karbon

Numerade Educator

Problem 84

Will help you prepare for the material covered in the next section.
Let $f(x)=3 x-4$ and $g(x)=x^{2}+6$
a. Find $f(5)$
b. Find $g(f(5))$.

AG

Ankit Gupta

Numerade Educator

Problem 85

Will help you prepare for the material covered in the next section.
Simplify: $3\left(\frac{x-2}{3}\right)+2$.

Brandon Fox

Numerade Educator

Problem 86

Will help you prepare for the material covered in the next section.
Solve for $y: \quad x=7 y-5$.

Alicia Amason

Numerade Educator