Intermediate Algebra (11th edition)

61.A sample of 400 g of lead 210 decays to polonium 210 according to the function defined by

where tis time in years. Approximate answers to the nearest hundredth.

(a)How much lead will be left in the sample after 25 yr?

(b)How long will it take the initial sample to decay to half of its original amount?

62.The concentration of a drug in a person’s system decreases according to the function

defined by

where is in appropriate units, and tis in hours. Approximate answers to the nearest

hundredth.

(a)How much of the drug will be in the system after 1 hr?

(b)Approximate the time it will take for the concentration to be half of its original amount.

63.Refer to Exercise 55.Assuming that the function continued to apply past 2007, in what

year can we expect the volume of materials recovered to reach 130 million tons? (Source:

Environmental Protection Agency.)

64.Refer to Exercise 56.Assuming that the function continued to apply past 2006, in what

year can we expect worldwide carbon dioxide emissions from fossil fuel consumption to

reach 34,000 million metric tons? (Source:U.S. Department of Energy.)

EXERCISES 65 – 66

65.The function defined by

with , described in Exercise 60,is graphed

on the screen at the right. Interpret the meanings

of X and Y in the display at the bottom of the

screen in the context of Exercise 60.

66.The screen shows a table of selected values for the

function defined by.

(a)Why is there an error message for?

(b)What number does the function value seem to

approach as X takes on larger and larger values?

(c)Use a calculator to evaluate this function for

. What value do you get? Now evaluate. How close are
these two values?
(d)Make a conjecture: As the values of xapproach infinity, the value of
approaches.

A^1 +

1

xB

x

X=1,000,000 e=e^1

X= 0

Y 1 = A 1 +X^1 BX

x=t

A 1 x 2 =3.25e-0.00043x,

TECHNOLOGY INSIGHTS

C 1 t 2

C 1 t 2 = 2 e-0.125t,

A 1 t 2 = 400 e-0.032t,

622 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions

5

0

0 1000

Graph each function. See Section 9.5.

67. 
    
    
    
    68. 69.ƒ 1 x 2 = 1 x+ 122 70.ƒ 1 x 2 = 1 x- 122 + 2
    
    
    
    

ƒ 1 x 2 = 2 x^2 ƒ 1 x 2 =x^2 - 1

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