1

In a Chapter 1 classroom example we looked at a function to calculate the cost to purchase custom printed lunch coolers for a school staff.

where is the total cost in dollars for purchasing L lunch coolers.a. What are the input and output variables for this function?

b. Find the inverse of this function.

6.1.1

( ) 45 3C L L ( )C L

2

c. What are the input and output variables for the inverse?

d. Find the cost to purchase 60 lunch coolers.

e. Find the number of lunch coolers you can purchase with a budget of $300.

6.1.1

1( ) 15

3L C C ( ) 45 3C L L

3

Find the inverse of the following functions.a. b.

6.1.2

( ) 4 20f x x 1( ) 7

5f x x

4

Graph the following functions. Use the horizontal line test to determine whether each function is a one-to-one function.

a.

b.

6.1.3

( ) 2 5f x x

2( ) 0.5 15 10g x x x

5

Graph the following functions. Use the horizontal line test to determine whether each function is a one-to-one function.

c.

d.

6.1.3

( ) 2.6(1.8)xf x

( ) 3h x

6

Perform the following compositions and simplify.

Let and

Find and

6.1.4

1 ( )f f x 1( )f f x

1 1( ) 5

4f x x ( ) 4 20f x x

7

Graph the following functions and their inverses. Include the graph of the line .a.

6.1.5

2( ) 8

3f x x 1 3

( ) 122

f x x

8

Graph the following functions and their inverses. Include the graph of the line .b.

6.1.5

5( )g x x 1 5( )g x x

9

Evaluate the following logarithms.a.

b.

6.2.1

3log 9

log10,000

10

Evaluate the following logarithms using the properties of logarithms.a.

b.

c.

6.2.2

83log 3

7log 1

8log 8

11

Use your calculator to evaluate the following logarithm.

a.

b.

6.2.3

log300

ln 24

12

Evaluate the following logarithms. Round your answers to three decimal places.

a.

b.

6.2.4

3log 470

7log 3.2

13

Rewrite the exponential equation into logarithm form.

a.

Rewrite the logarithm equation into exponential form.

b.

6.2.5

56 7776

7log 2401 4

14

Find the inverses for the following functions.a. b.

6.2.6

( ) 5xf x ( ) lnf x x

15

Find the inverses for the following functions.c.

6.2.6

( ) 3(2)xf x

16

Solve each logarithm equation by rewriting it in exponential form.

a. b.

6.2.7

log 4x 5log 3x

17

Sketch the graph of

6.3.1

4( ) logf x x

18

Sketch the graph of

6.3.2

1/3( ) logf x x

19

Give the domain and range of

6.3.3

1/3( ) logf x x

20

Expand the following logarithms as separate simpler logarithms.

a.

b.

6.4.1

3log 7x

52

loga

c

21

Write the following logarithms as a single logarithm.

a.

b.

6.4.2

log3 log( 5)a

ln 4 ln 5x y

22

Expand the following logarithms as separate simpler logarithms.a.

b.

6.4.3

3 27log 4a b

5

3

2log

x

y

23

Expand the following logarithms as separate simpler logarithms.c.

6.4.3

3 9ln 11a b c

24

Write the following logarithms as a single logarithm.

a.

b.

6.4.4

2 2 2log 7 4log 2loga b

2ln 4 3ln 5lnx z y

25

Write the following logarithms as a single logarithm. c.

6.4.4

1 7 3log5 log log2 2 2

a c

26

Solve

6.5.1

3 14x

27

Compute-4-You started business in 2002 and revenue grew rapidly after that. Revenue for several years are given in the table.

a. Write an equation for a model of these data.

6.5.2

Year 2005 2006 2007 2008 2009 2010

Revenue (million $) 2.1 3.68 6.43 11.26 19.7 34.48

28

b. Find when the revenue will reach $100 million.

6.5.2

( ) 0.128(1.75)tR t

29

Solve the following exponential equations. Round your answers to three decimal places.a. b.

6.5.3

48 10 47x 75(3) 30x

30

Solve the following exponential equations. Round your answers to three decimal places.c.

6.5.3

2 54 256x

31

In section 5.5 we found the model for the gross domestic product of Madagascar. Where = the GDP of Madagascar in billions of US$. t = years since 2005.

Find the year that Madagascar’s GDP will be $25 billion.

6.5.4

( ) 16.9(1.06)tM t

( )M t

32

Hayes Inc. has $40,000 to invest. They need to double their money in 12 years to replace a piece of equipment that they rely on for their business. Find the annual interest rate compounded daily that they need in order to double their money in 12 years.

6.5.5

33

If a deposit of $3,000 is invested in an account paying 5% compounded weekly, how long will it take to double in value.

6.5.6

34

If $5000 is invested in a Certificate of Deposit (CD) that pays 3% annual interest compounded continuously, how long will it take for the investment to double?

6.5.7

35

Solve the logarithm equation

6.6.1

log( 10) 3x

36

If the intensity of an earthquake were 60,000 cm, what would its magnitude be?

6.6.2

37

What is the intensity of an earthquake of magnitude 8.2?

6.6.3

38

What is the pH of an aqueous solution when the concentration of hydrogen ions is M?

6.6.4

47.4 10

39

Find the hydrogen ion concentration of a solution with a pH of 3.8.

6.6.5

40

Solve the following logarithm equations. Round your answers to three decimal places.a. b.

 

6.6.6

ln 5x 4log (5 ) 10 13x

41

Solve the following logarithm equations. Round your answers to three decimal places.a. b.

 

6.6.7

3 3log log (6 ) 4x x ln(5 7) 6x

42

Solve the following logarithm equations. Round your answers to three decimal places.c.

6.6.7

5 5log ( 3) log ( 7) 1x x