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Precalculus with Limits

Ron Larson

Chapter 3

Exponential and Logarithmic Functions - all with Video Answers

Educators

WZ

Section 1

Exponential Functions and Their Graphs

00:29

Problem 1

Fill in the blanks.

Polynomial and rational functions are examples of ________ functions.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:29

Problem 2

Fill in the blanks.

Exponential and logarithmic functions are examples of nonalgebraic functions, also called ________ functions.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:30

Problem 3

Fill in the blanks.

You can use the ________ Property to solve simple exponential equations.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:30

Problem 4

Fill in the blanks.

The exponential function given by $ f(x) = e^x $ is called the ________ ________ function,and the base $ e $ is called the ________ base.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:33

Problem 5

Fill in the blanks.

To find the amount $ A $ in an account after $ t $ years with principal $ P $ and an annual interest rate $ r $ compounded $ n $ times per year, you can use the formula ________.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:30

Problem 6

Fill in the blanks.

To find the amount $ A $ in an account after $ t $ years with principal $ P $ and an annual interest rate $ r $ compounded continuously, you can use the formula ________.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:31

Problem 7

In Exercises 7 - 12, evaluate the function at the indicated value of Round your result to three decimal places.

Function
$ f(x) = 0.9^x $

Value
$ x = 1.4 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:32

Problem 8

In Exercises 7 - 12, evaluate the function at the indicated value of Round your result to three decimal places.

Function
$ f(x) = 2.3^x $

Value
$ x = \dfrac{2}{3} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:33

Problem 9

In Exercises 7 - 12, evaluate the function at the indicated value of Round your result to three decimal places.

Function
$ f(x) = 5^x $

Value
$ x = - \pi $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:46

Problem 10

In Exercises 7 - 12, evaluate the function at the indicated value of Round your result to three decimal places.

Function
$ f(x) = \left(\dfrac{2}{3}\right)^{5x} $

Value
$ x = \dfrac{3}{10} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:42

Problem 11

In Exercises 7 - 12, evaluate the function at the indicated value of Round your result to three decimal places.

Function
$ g(x) = 5000(2^x) $

Value
$ x = -1.5 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:59

Problem 12

In Exercises 7 - 12, evaluate the function at the indicated value of Round your result to three decimal places.

Function
$ f(x) = 200(1.2)^{12x} $

Value
$ x = 24 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:26

Problem 13

In Exercises 13 - 16, match the exponential function with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$ f(x) = 2^x $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:38

Problem 14

In Exercises 13 - 16, match the exponential function with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$ f(x) = 2^x + 1 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:52

Problem 15

In Exercises 13 - 16, match the exponential function with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$ f(x) = 2^{-x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:39

Problem 16

In Exercises 13 - 16, match the exponential function with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$ f(x) = 2^{x - 2} $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:10

Problem 17

In Exercises 17 - 22, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = \left(\dfrac{1}{2}\right)^x $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:03

Problem 18

In Exercises 17 - 22, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = \left(\dfrac{1}{2}\right)^{-x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:53

Problem 19

In Exercises 17 - 22, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = 6^{-x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:45

Problem 20

In Exercises 17 - 22, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = 6^x $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:49

Problem 21

In Exercises 17 - 22, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = 2^{x - 1} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:47

Problem 22

In Exercises 17 - 22, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = 4^{x - 3} + 3 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:45

Problem 23

In Exercises 23 - 28, use the graph of $ f $ to describe the transformation that yields the graph of $ g $.

$ f(x) = 3^x $, $ g(x) = 3^x + 1 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:49

Problem 24

In Exercises 23 - 28, use the graph of $ f $ to describe the transformation that yields the graph of $ g $.

$ f(x) = 4^x $, $ g(x) = 4^{x - 3} $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:19

Problem 25

In Exercises 23 - 28, use the graph of $ f $ to describe the transformation that yields the graph of $ g $.

$ f(x) = 2^x $, $ g(x) = 3 - 2 $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:31

Problem 26

In Exercises 23 - 28, use the graph of $ f $ to describe the transformation that yields the graph of $ g $.

$ f(x) = 10^x $, $ g(x) = 10^{-x + 3} $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:39

Problem 27

In Exercises 23 - 28, use the graph of $ f $ to describe the transformation that yields the graph of $ g $.

$ f(x) = \left(\dfrac{7}{2}\right)^x $, $ g(x) = -\left(\dfrac{7}{2}\right)^{-x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
02:06

Problem 28

In Exercises 23 - 28, use the graph of $ f $ to describe the transformation that yields the graph of $ g $.

$ f(x) = 0.3^x $, $ g(x) = 0.3^x + 5 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:35

Problem 29

In Exercises 29 - 32, use a graphing utility to graph the exponential function.

$ y = 2^{-x^2} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:38

Problem 30

In Exercises 29 - 32, use a graphing utility to graph the exponential function.

$ y = 3^{-\mid x \mid} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:39

Problem 31

In Exercises 29 - 32, use a graphing utility to graph the exponential function.

$ y = 3^{x - 2} + 1 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:36

Problem 32

In Exercises 29 - 32, use a graphing utility to graph the exponential function.

$ y = 4^{x + 1} - 2 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:48

Problem 33

In Exercises 33 - 38, evaluate the function at the indicated value of $ x $. Round your result to three decimal places.

Function
$ h(x) = e^{-x} $

Value
$ x = \dfrac{3}{4} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:41

Problem 34

In Exercises 33 - 38, evaluate the function at the indicated value of $ x $. Round your result to three decimal places.

Function
$ f(x) = e^{x} $

Value
$ x = 3.2 $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:10

Problem 35

In Exercises 33 - 38, evaluate the function at the indicated value of $ x $. Round your result to three decimal places.

Function
$ f(x) = 2e^{-5x} $

Value
$ x = 10 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:58

Problem 36

In Exercises 33 - 38, evaluate the function at the indicated value of $ x $. Round your result to three decimal places.

Function
$ f(x) = 1.5e^{x/2} $

Value
$ x = 240 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:47

Problem 37

In Exercises 33 - 38, evaluate the function at the indicated value of $ x $. Round your result to three decimal places.

Function
$ h(x) = 5000e^{0.06x} $

Value
$ x = 6 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:50

Problem 38

In Exercises 33 - 38, evaluate the function at the indicated value of $ x $. Round your result to three decimal places.

Function
$ f(x) = 250e^{0.05x} $

Value
$ x = 20 $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:00

Problem 39

In Exercises 39 - 44, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = e^x $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:06

Problem 40

In Exercises 39 - 44, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = e^{-x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:30

Problem 41

In Exercises 39 - 44, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = 3e^{x + 4} $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:18

Problem 42

In Exercises 39 - 44, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = 2e^{-0.5x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:08

Problem 43

In Exercises 39 - 44, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = 2e^{x - 2} + 4 $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:12

Problem 44

In Exercises 39 - 44, use a graphing utility to construct a table of values for the function. Then sketch the graph of the function.

$ f(x) = 2 + e^{x - 5} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:37

Problem 45

In Exercises 45 - 50, use a graphing utility to graph the exponential function.

$ y = 1.08^{-5x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:40

Problem 46

In Exercises 45 - 50, use a graphing utility to graph the exponential function.

$ y = 1.08^{5x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:45

Problem 47

In Exercises 45 - 50, use a graphing utility to graph the exponential function.

$ s(t) = 2e^{0.12t} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:44

Problem 48

In Exercises 45 - 50, use a graphing utility to graph the exponential function.

$ s(t) = 3e^{0.2t} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:36

Problem 49

In Exercises 45 - 50, use a graphing utility to graph the exponential function.

$ g(x) = 1 + e^{-x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:38

Problem 50

In Exercises 45 - 50, use a graphing utility to graph the exponential function.

$ h(x) = e^{x - 2} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:22

Problem 51

In Exercises 51 - 58, use the One-to-One Property to solve the equation for $ x $.

$ 3^{x + 1} = 27 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:23

Problem 52

In Exercises 51 - 58, use the One-to-One Property to solve the equation for $ x $.

$ 2^{x - 3} = 16 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:33

Problem 53

In Exercises 51 - 58, use the One-to-One Property to solve the equation for $ x $.

$ \left(\dfrac{1}{2}\right)^x = 32 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:33

Problem 54

In Exercises 51 - 58, use the One-to-One Property to solve the equation for $ x $.

$ 5^{x - 2} = \dfrac{1}{125} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:19

Problem 55

In Exercises 51 - 58, use the One-to-One Property to solve the equation for $ x $.

$ e^{3x + 2} = e^3 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:19

Problem 56

In Exercises 51 - 58, use the One-to-One Property to solve the equation for $ x $.

$ e^{2x - 1} = e^4 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:40

Problem 57

In Exercises 51 - 58, use the One-to-One Property to solve the equation for $ x $.

$ e^{x^2 - 3} = e^{2x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:37

Problem 58

In Exercises 51 - 58, use the One-to-One Property to solve the equation for $ x $.

$ e^{x^2 + 6} = e^{5x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
03:15

Problem 59

In Exercises 59 - 62, complete the table to determine the balance $ A $ for $ P $ dollars invested at rate $ r $ for $ t $ years and compounded $ n $ times per year.

$ P = \$1500 $, $ r = 2\% $, $ t = 10 $ years

Heather Zimmers
Heather Zimmers
Numerade Educator
02:20

Problem 60

In Exercises 59 - 62, complete the table to determine the balance $ A $ for $ P $ dollars invested at rate $ r $ for $ t $ years and compounded $ n $ times per year.

$ P = \$2500 $, $ r = 3.5\% $, $ t = 10 $ years

Heather Zimmers
Heather Zimmers
Numerade Educator
02:12

Problem 61

In Exercises 59 - 62, complete the table to determine the balance $ A $ for $ P $ dollars invested at rate $ r $ for $ t $ years and compounded $ n $ times per year.

$ P = \$2500 $, $ r = 4\% $, $ t = 20 $ years

Heather Zimmers
Heather Zimmers
Numerade Educator
02:26

Problem 62

In Exercises 59 - 62, complete the table to determine the balance $ A $ for $ P $ dollars invested at rate $ r $ for $ t $ years and compounded $ n $ times per year.

$ P = \$1000 $, $ r = 6\% $, $ t = 40 $ years

Heather Zimmers
Heather Zimmers
Numerade Educator
01:33

Problem 63

In Exercises 63 - 66, complete the table to determine the balance $ A $ for $ \$12,000 $ invested at rate $ r $ for $ t $ years, compounded continuously.

$ r = 4\% $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:39

Problem 64

In Exercises 63 - 66, complete the table to determine the balance $ A $ for $ \$12,000 $ invested at rate $ r $ for $ t $ years, compounded continuously.

$ r = 6\% $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:39

Problem 65

In Exercises 63 - 66, complete the table to determine the balance $ A $ for $ \$12,000 $ invested at rate $ r $ for $ t $ years, compounded continuously.

$ r = 6.5\% $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:28

Problem 66

In Exercises 63 - 66, complete the table to determine the balance $ A $ for $ \$12,000 $ invested at rate $ r $ for $ t $ years, compounded continuously.

$ r = 3.5\% $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:09

Problem 67

On the day of a childs birth, a deposit of $ \$30,000 $ is made in a trust fund that pays $ 5\% $ interest,compounded continuously. Determine the balance in this account on the childs 25th birthday.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:55

Problem 68

A deposit of $ \$5000 $ is made in a trust fund that pays $ 7.5\% $ interest, compounded continuously.It is specified that the balance will be given to the college from which the donor graduated after the money has earned interest for $ 50 $ years. How much will the college receive?

Heather Zimmers
Heather Zimmers
Numerade Educator
00:55

Problem 69

If the annual rate of inflation averages $ 4\% $ over the next $ 10 $ years, the approximate costs $ C $ of goods or services during any year in that decade will be modeled by $ C(t) = P(1.04)^t $, where $ t $ is the time in years and $ P $ is the present cost. The price of an oil change for your car is presently $ \$23.95 $. Estimate the price $ 10 $ years from now.

Heather Zimmers
Heather Zimmers
Numerade Educator
01:22

Problem 70

The number $ V $ of computers infected by a computer virus increases according to the model $ V(t) = 100e^{4.6052t} $, where $ t $ is the time in hours.Find the number of computers infected after (a) $ 1 $ hour,(b) $ 1.5 $ hours, and (c) $ 2 $ hours.

Heather Zimmers
Heather Zimmers
Numerade Educator
03:36

Problem 71

The projected populations of California for the years $ 2015 $ through $ 2030 $ can be modeled by $ P = 34.696e^{0.0098} $, where $ P $ is the population (in millions) and $ t $ is the time (in years), with $ t = 15 $ corresponding to $ 2015 $.(Source: U.S. Census Bureau)

(a) Use a graphing utility to graph the function for the years $ 2015 $ through $ 2030 $.
(b) Use the table feature of a graphing utility to create a table of values for the same time period as in part (a).
(c) According to the model, when will the population of California exceed $ 50 $ million?

Heather Zimmers
Heather Zimmers
Numerade Educator
02:07

Problem 72

The population $ P $ (In millions) of Italy from $ 1990 $ through $ 2008 $ can be approximated by the model $ P = 56.8e^{0.0015t} $, where $ t $ represents the year,with $ t = 0 $ corresponding to $ 1990 $.(Source: U.S.Census Bureau, International Data Base)

(a) According to the model, is the population of Italy increasing or decreasing? Explain.
(b) Find the populations of Italy in $ 2000 $ and $ 2008 $.
(c) Use the model to predict the populations of Italy in $ 2015 $ and $ 2020 $

Heather Zimmers
Heather Zimmers
Numerade Educator
02:25

Problem 73

Let $ Q $ represent a mass of radioactive plutonium $ \left(^{239}Pu\right) $ (in grams), whose half-life is $ 24,100 $ years. The quantity of plutonium present after years is $ Q = 16 \left(\dfrac{1}{2}\right)^{t/24,100} $

(a) Determine the initial quantity (when $ t = 0 $).

(b) Determine the quantity present after $ 75,000 $ years.

(c) Use a graphing utility to graph the function over the interval $ t = 0 $ to $ t = 150,000 $.

Heather Zimmers
Heather Zimmers
Numerade Educator
01:33

Problem 74

Let $ Q $ represent a mass of carbon $ 14 \left(^{14}C\right) $ (in grams), whose half-life is $ 5715 $ years.The quantity of carbon $ 14 $ present after $ t $ years is

$ Q = 10\left(\dfrac{1}{2}\right)^{t/5715} $

(a) Determine the initial quantity (when $ t = 0 $).
(b) Determine the quantity present after $ 2000 $ years.
(c) Sketch the graph of this function over the interval $ t = 0 $ to $ t = 10,000 $.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:57

Problem 75

After $ t $ years, the value of a wheel-chair conversion van that originally cost $ \$30,500 $ depreciates so that each year it is worth $ \dfrac{7}{8} $ of its value for the previous year.

(a) Find a model for $ V(t) $, the value of the van after $ t $ years.
(b) Determine the value of the van $ 4 $ years after it was purchased.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:49

Problem 76

Immediately following an injection, the concentration of a drug in the bloodstream is $ 300 $ milligrams per milliliter. After $ t $ hours, the concentration is $ 75\% $ of the level of the previous hour.

(a) Find a model for $ C(t) $, the concentration of the drug after $ t $ hours.
(b) Determine the concentration of the drug after $ 8 $ hours.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:52

Problem 77

In Exercises 77 and 78, determine whether the statement is true or false. Justify your answer.

The line $ y = -2 $ asymptote for the graph of

$ f(x) = 10^x - 2 $.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:32

Problem 78

In Exercises 77 and 78, determine whether the statement is true or false. Justify your answer.

$ e = \dfrac{271,801}{99,990} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:40

Problem 79

In Exercises 79 - 82, use properties of exponents to determine which functions (if any) are the same.

$ f(x) = 3^{x - 2} $
$ g(x) = 3^x - 9 $
$ h(x) = \dfrac{1}{9}\left(3^x\right) $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:46

Problem 80

In Exercises 79 - 82, use properties of exponents to determine which functions (if any) are the same.

$ f(x) = 4^x + 12 $
$ g(x) = 2^{2x + 6} $
$ h(x) = 64\left(4x\right) $

Heather Zimmers
Heather Zimmers
Numerade Educator
02:03

Problem 81

In Exercises 79 - 82, use properties of exponents to determine which functions (if any) are the same.

$ f(x) = 16\left(4^{-x}\right) $
$ g(x) = \left(\dfrac{1}{4}\right)^{x - 2} $
$ h(x) = 16\left(2^{-2x}\right) $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:22

Problem 82

In Exercises 79 - 82, use properties of exponents to determine which functions (if any) are the same.

$ f(x) = e^{-x} + 3 $
$ g(x) = e^{3 - x} $
$ h(x) = -e^{x - 3} $

Heather Zimmers
Heather Zimmers
Numerade Educator
01:03

Problem 83

Graph the functions given by $ y = 3^x $ and $ y = 4^x $ and use the graphs to solve each inequality.

(a) $ 4^x < 3^x $

(b) $ 4^x > 3^x $

Heather Zimmers
Heather Zimmers
Numerade Educator
02:58

Problem 84

Use a graphing utility to graph each function. Use the graph to find where the function is increasing and decreasing, and approximate any relative maximum or minimum values.

(a) f(x) = x^2e^{-x} $

(b) g(x) = x2^{3 - x} $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:55

Problem 85

Use a graphing utility to graph $ y_1 = \left(1 + 1/x\right)^x $ and $ y_2 = e $ in the same viewing window. Using the trace feature, explain what happens to the graph $ y_1 $ as $ x $ increases.

Heather Zimmers
Heather Zimmers
Numerade Educator
01:04

Problem 86

Use a graphing utility to graph

$ f(x) = \left(1 + \dfrac{0.5}{x}\right)^x $ and $ g(x) = e^{0.5} $

in the same viewing window. What is the relationship between $ f $ and $ g $ as $ x $ increases and decreases without bound?

Heather Zimmers
Heather Zimmers
Numerade Educator
01:51

Problem 87

Use a graphing utility to graph each pair of functions in the same viewing window.Describe any similarities and differences in the graphs.

(a) $ y_1 = 2^x $, $ y_2 = x^2 $

(b) $ y_1 = 3^x $, $ y_2 = x^3 $

Heather Zimmers
Heather Zimmers
Numerade Educator
00:48

Problem 88

THINK ABOUT IT Which functions are exponential?
(a) $3 x$
(b) $3 x^2$
(c) $3^x$
(d) $2^{-x}$

Heather Zimmers
Heather Zimmers
Numerade Educator
02:48

Problem 89

Use the formula

$ A = P \left(1 + \dfrac{r}{n}\right)^{nt} $

to calculate the balance of an account when $ P = \$3000 $, $ r = 6\% $ and $ t = 10 $ and compounding is done (a) by the day, (b) by the hour, (c) by the minute, and(d) by the second. Does increasing the number of compoundings per year result in unlimited growth of the balance of the account? Explain.

Heather Zimmers
Heather Zimmers
Numerade Educator
01:11

Problem 90

The figure shows the graphs of $ y = 2^x $, $ y = e^x $, $ y = 10^x $, $ y = 2^{-x} $, $ y = e^{-x} $, and $ y = 10^{-x} $. Match each function with its graph. [The graphs are labeled (a) through (f).] Explain your reasoning.

Heather Zimmers
Heather Zimmers
Numerade Educator