Intermediate Algebra (11th edition)

Solve each problem. See Example 9.

55.The total volume in millions of tons of materials recovered from municipal solid waste
collections in the United States during the period 1980 –2007 can be approximated by the
function defined by

where corresponds to 1980, to 1981, and so on. Approximate, to the nearest

tenth, the volume recovered each year. (Source:U.S. Environmental Protection Agency.)

(a) 1980 (b) 1990 (c) 2000 (d) 2007

56.Worldwide emissions in millions of metric tons of the greenhouse gas carbon dioxide
from fossil fuel consumption during the period 1990–2006 can be modeled by the func-
tion defined by

where corresponds to 1990, to 1991, and so on. Approximate, to the nearest

unit, the emissions for each year. (Source:U.S. Department of Energy.)

(a) 1990 (b) 1995 (c) 2000 (d) 2006

57.Revenues of software publishers in the United States for the years 2004 –2007 can be
modeled by the function defined by

where represents 2004, represents 2005, and so on, and is in millions of

dollars. Approximate, to the nearest unit, consumer expenditures for 2007. (Source:U.S.

Census Bureau.)

58.Based on selected figures obtained during the
years 1980 –2007, the total number of bachelor’s
degrees earned in the United States can be mod-
eled by the function defined by

where corresponds to 1980, cor-

responds to 1990, and so on. Approximate, to the

nearest unit, the number of bachelor’s degrees

earned in 2005. (Source:U.S. National Center

for Education Statistics.)

59.Suppose that the amount, in grams, of plutonium 241 present in a given sample is deter-
mined by the function defined by

where tis measured in years. Approximate the amount present, to the nearest hundredth,

in the sample after the given number of years.

(a) 4 (b) 10 (c) 20 (d)What was the initial amount present?

60.Suppose that the amount, in grams, of radium 226 present in a given sample is determined
by the function defined by

where tis measured in years. Approximate the amount present, to the nearest hundredth,

in the sample after the given number of years.

(a) 20 (b) 100 (c) 500 (d)What was the initial amount present?

A 1 t 2 =3.25e-0.00043t,

A 1 t 2 =2.00e-0.053t,

x= 0 x= 10

D 1 x 2 =900,584e0.0185x,

x= 0 x= 1 S 1 x 2

S 1 x 2 =112,047e0.0827x,

x= 0 x= 1

ƒ 1 x 2 =20,761e0.01882x,

x= 0 x= 1

ƒ 1 x 2 =15.94e0.0656x,

SECTION 10.6 Exponential and Logarithmic Equations; Further Applications 621