copyright © 2009 pearson education, inc. slide 5 - 1 active learning lecture slides for use with...

Copyright © 2009 Pearson Education, Inc. Slide 5 - 1

Active Learning Lecture SlidesFor use with Classroom Response Systems

© 2009 Pearson Education, Inc.

Chapter 5Exponential

and Logarithmic Functions


CHAPTER 5: Exponential and

Logarithmic Functions5.1 Inverse Functions5.2 Exponential Functions and Graphs5.3 Logarithmic Functions and Graphs

5.4 Properties of Logarithmic Functions

5.5 Solving Exponential and Logarithmic Equations

5.6 Applications and Models: Growth and Decay; and

Compound Interest


Find the inverse of the relation

a.

c.

b.

d.

3,2 , 4,0 , 5,1 , 1, 6

3, 2 , 4,0 , 5, 1 , 1,6 .

2, 3 , 0, 4 , 1,5 , 6,1

2,3 , 0,4 , 1, 5 , 6, 1

1 1 1 1 1, , ,0 , , 1 , 1,

3 2 4 5 6



a.

c.

b.

d.

3,2 , 4,0 , 5,1 , 1, 6

3, 2 , 4,0 , 5, 1 , 1,6 .

2, 3 , 0, 4 , 1,5 , 6,1

2,3 , 0,4 , 1, 5 , 6, 1

1 1 1 1 1, , ,0 , , 1 , 1,

3 2 4 5 6



a.

c.

b.

d.

4,2 , 0, 5 , 5,3 , 1, 7

2,4 , 5,0 , 3, 5 , 7,1 .

4, 2 , 0,5 , 5, 3 , 1,7

2, 4 , 5,0 , 3,5 , 7, 1

1 1 1 1 1 1, , ,0 , , , ,1

2 4 5 3 5 6


Find a formula for the inverse of the function f(x) = 10 – 6x.

a.

c.

b.

d.

1 6 10f x x

1 6

10

xf x

1 10

6

xf x

1 5

3f x x


Find a formula for the inverse of the function f(x) = 2x+5.

a.

c.

b.

d.

1 5

2

xf x

1 15

2f x x

1 5 2f x x

1 5

2

xf x


Which of the following functions is one-to-one?

a. b.

c. d.

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0


Which of the following graphs illustrates the graph of f(x) = 4x.

a. b.

c. d.

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0


Which of the following graphs illustrates the graph of f(x) = –2x – 1.

a. b.

c. d.

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0

X

Y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

0


Find the approximate value of e0.16 to four decimal places.

a. –1.1735

c. 0.8521

b. –0.8521

d. 1.0161


Find the approximate value of e–0.16 to four decimal places.

a. –1.1735

c. 0.8521

b. –0.8521

d. 1.0161


Using the compound interest formula,

determine the approximate amount in the account after 5 years if the investment is $1500 at an

interest rate of 8.2% compounded quarterly.

a. $2195.64

c. $2260.23

b. $2250.88

d. $2271.56

1nt

rA P

n


Suppose a school deposited a $1000 scholarship in an account paying 7.9% interest compounded quarterly. Approximately how much will the scholarship be worth in two years?

a. $1169.36

c. $1268.77

b. $1250.98

d. $1316.42


Convert to a logarithmic equation: 2x = 20.

a. x = log220

c. 2 = logx20

b. x = log10

d. x = log202


Convert to an exponential equation: log3x = 5.

a. x = 53

c. x5 = 3

b. x = 35

d. x3 = 5


Find ln 3 using a calculator. Round to four decimal places.

a. 0.4771

c. 20.0855

b. 1.0986

d. 1000


Find log 0.001. Do not use a calculator.

a. –4

c. 3

b. –3

d. 1000


Find log58 using the change-of-base formula.

a. 0.2041

c. 1.2920

b. 0.7740

d. 1.6


Express in terms of sums and

differences of logarithms:

a.

c.

b.

d.

2

3log .x

y

1 1log log

9 3x y

6log 3logx y

2 1log log

3 3x y

2log log

3x y




a.

c.

b.

d.

2

3log .x

y

1 1log log

9 3x y

6log 3logx y

2 1log log

3 3x y

2log log

3x y




a.

c.

b.

d.

35log .y z

3log log

5y z

5log 5log

3y z

5log3 5logy z

3 1log log

5 5y z


Given that logc2 = 0.3333 and logc12 = 1.1950, find logc6.

a. 3.5854

c. 0.8617

b. 0.9999

d. 0.1951


Given that loga3 = 0.6826 and loga4 = 0.8614, find loga36.

a. 0.4014

c. 2.2266

b. 1.1760

d. 4.6320


Simplify: lne6t.

a. e-6t

c. 6t

b. te6

d. –6t


Solve: log3(3x + 6) – log3(x – 6) = 2.

a. 14

c.

b. 10

d. Does not exist

3

2


Solve: log2(x + 5) + log2(x – 1) = 4.

a.

c. 5

b. 3

d. 6

1

3


Solve: log2(x – 3) + log2(2x – 10) = 4.

a. 4

c.

b. 7

d. No solution

29

3


Solve: 25+x = 32x-4.

a.

c.

b.

d. 25

4

69

15

9

4

15

4


Solve: 35+4x = 9x.

a.

c.

b. –5

d.

5

2

5

3

5

3


The population of a city doubled in 12 years. What was the approximate exponential growth rate?

a. 16.7%

c. 5.8%

b. 6.0%

d. 2.48%



a. 16.7%

c. 5.8%

b. 6.0%

d. 2.48%



a. 3.0%

c. 6.9%

b. 5.0%

d. 14.4%


Suppose $2000 is invested at interest rate, k, compounded continuously, and grows to $2,473.53 in 5 years. Find the approximate interest rate.

a. 3.83%

c. 4.75%

b. 4.25%

d. 7.89%


Suppose $2000 is invested at interest rate, k, compounded continuously, and grows to $2.473.53 in 5 years. Find the approximate interest rate.

a. 3.83%

c. 4.75%

b. 4.25%

d. 7.89%


Suppose $2000 is invested at interest rate, k, compounded continuously, and grows to $2.473.53 in 5 years. Find the approximate doubling time.

a. 7.1 years

c. 16.3 years

b. 14.6 years

d. 21.1 years


Suppose $8000 is invested at interest rate, k, compounded continuously, and grows to $10,962.07 in 5 years. Approximate the amount in the account after 10 years.

a. $13,924.14

c. $15,020.87

b. $14,259.22

d. $15,664.41

copyright © 2009 pearson education, inc. slide 5 - 1 active learning lecture slides for use with...

Documents