Solve each problem. See Example 6.
61.For 1981–2003, the number of billion cubic feet of natural gas gross withdrawals from
crude oil wells in the United States can be approximated by the function defined by
where corresponds to 1981, to 1982, and so on. (Source:Energy Informa-
tion Administration.) Use this function to approximate, to the nearest unit, the number of
cubic feet withdrawn in each of the following years.
(a) 1982 (b) 1988 (c) 1996
62.According to selected figures from the last two decades of the 20th century, the number of
trillion cubic feet of dry natural gas consumed worldwide can be approximated by the
function defined by
where corresponds to 1980, to 1981, and so on. (Source:Energy Informa-
tion Administration.) Use the function to approximate, to the nearest hundredth, con-
sumption in each year.
(a) 1980 (b) 1987 (c) 1995
63.Sales (in thousands of units) of a new product are approximated by the function defined by
where tis the number of years after the product is introduced.
(a)What were the sales, to the nearest unit, after 1 yr?
(b)What were the sales, to the nearest unit, after 13 yr?
(c) Graph.
64.A study showed that the number of mice in an old abandoned house was approximated by
the function defined by
where tis measured in months and corresponds to January 2008. Find the number
of mice in the house in
(a)January 2008 (b)July 2008 (c)July 2010.
(d) Graph the function.
The Richter scaleis used to measure the
intensity of earthquakes. The Richter scale
rating of an earthquake of intensity x is
given by
where is the intensity of an earthquake
of a certain (small) size. The figure here
shows Richter scale ratings for Southern
California earthquakes from 1930 to
2000 with magnitudes greater than 4.7.
65.The 1994 Northridge earthquake had
a Richter scale rating of 6.7. The
1992 Landers earthquake had a rating
of 7.3. How much more powerful was
the Landers earthquake than the
Northridge earthquake?
66.Compare the smallest rated earthquake in the figure (at 4.8) with the Landers quake. How
much more powerful was the Landers quake?
x 0
R=log 10
x
x 0
,
t= 0
M 1 t 2 =6 log 4 12 t+ 42 ,
y=S 1 t 2
S 1 t 2 = 100 +30 log 3 12 t+ 12 ,
x= 1 x= 2
ƒ 1 x 2 =51.47+6.044 log 2 x,
x= 1 x= 2
ƒ 1 x 2 = 3800 +585 log 2 x,
594 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions
Southern California Earthquakes
Year
Source: Caltech; U.S. Geological Survey.
’30 ’40 ’50 ’60 ’70 ’80 ’90 ’0 0
Magnitude
4.0
4.5
5.0
5.5
6.0
6.5
- 5
Long Beach,
1933
San Fernando,
1971
Landers,
1992
Hector Mine,
1999
Northridge,
1994
8.0
(with magnitudes greater than 4.7)
