Intermediate Algebra (11th edition)

Solve each problem. See Examples 6 and 7.

37.Based on figures from 1970 through 2005, the worldwide carbon dioxide emissions in
millions of metric tons are approximated by the exponential function defined by

where corresponds to 1970, corresponds to 1975, and so on. (Source:Car-

bon Dioxide Information Analysis Center.) Give answers to the nearest unit.

(a)Use this model to approximate the emissions in 1980.

(b)Use this model to approximate the emissions in 1995.

(c) In 2000, the actual amount of emissions was 6735 million tons. How does this

compare to the number that the model provides?

38.Based on figures from 1980 through 2007, the municipal solid waste generated in mil-
lions of tons can be approximated by the exponential function defined by

where corresponds to 1980, corresponds to 1985, and so on. (Source:U.S.

Environmental Protection Agency.) Give answers to the nearest hundredth.

(a)Use the model to approximate the number of tons of this waste in 1980.

(b)Use the model to approximate the number of tons of this waste in 1995.

(c) In 2007, the actual number of millions of tons of this waste was 254.1. How does this

compare to the number that the model provides?

39.A small business estimates that the value of a
copy machine is decreasing according to the func-
tion defined by

where tis the number of years that have elapsed since

the machine was purchased, and is in dollars.

(a)What was the original value of the machine?

(b)What is the value of the machine 5 yr after

purchase, to the nearest dollar?

(c) What is the value of the machine 10 yr after purchase, to the nearest dollar?

(d)Graph the function.

40.The amount of radioactive material in an ore sample is given by the function defined by

where is the amount present, in grams, of the sample tmonths after the initial meas-

urement.

(a)How much was present at the initial measurement? (Hint: .)

(b)How much was present 2 months later?

(c) How much was present 10 months later?

(d)Graph the function.

41.Refer to the function in Exercise 39.When will the value of the machine be $2500?
(Hint:Let , divide both sides by 5000, and use the method of Example 4.)

42.Refer to the function in Exercise 39.When will the value of the machine be $1250?

V 1 t 2 = 2500

t= 0

A 1 t 2

A 1 t 2 = 1001 3.2 2 - 0.5t,

V 1 t 2

V 1 t 2 = 5000122 - 0.15t,

V 1 t 2

x= 0 x= 5

ƒ 1 x 2 =159.51 1 1.0186 2 x,

x= 0 x= 5

ƒ 1 x 2 = 42311 1.0174 2 x,

SECTION 10.2 Exponential Functions 587

Determine what number would have to be placed in each box for the statement to be true. See
Sections 5.1 and 8.2.

43. 
    
    
    
    44. 2 n= 45. 2 n= 1 46. 2 n= 22
    
    
    
    

1

16

2 n= 16

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