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212 Chapter 3 Exponential and Logarithmic Functions
96.
t 16.625 ln
x
x 750 , x > 750
(a)
16.625 ln
897.72
30 years
897.72 750
97.
y 80.4 11 ln x
y300 80.4 11 ln 300 17.66 ft 3 min
30
16.625 ln
1659.24
10 years
1659.24 750
(b)
897.723012 323,179.20
1659.241012 199,108.80
100
0
1500
Interest for 30-year loan is
323,179.20 150,000 173,179.20.
Interest for 10-year loan is
199,108.80 150,000 49,108.80.
98.
y 80.4 11 ln x, 100 ≤ x ≤ 1500
450 cubic ft per minute
(a)
15 cubic feet per minute per child
30 children
(b) From the graph, for y 15 you get x 382 cubic feet.
(c) If ceiling height is 30, then 382 square feet of floor space is needed.
99. False. You would reflect y 6 x in the line y x.
100. True. log 3 27 log 3 3 3 3
101.
5 log b 32 102.
b 5 32 2 5
b 2
4 log b 81 103.
b 4 81 3 4
b 3
2 log b 1 16 104.
b 2 1 16 1 4 2
b 1 4
3 log b 27
1
b 3 1 27 1 3 3
b 1 3
105. The vertical asymptote is to the right of the y-axis,
and the graph increases. Matches (b).
106. The vertical asymptote is to the left of the y-axis.
Matches (b).
107. f x log is the inverse of gx a x a x
, where a > 0, a 1.
108. (a)
(b)
f x ln x, gx x 109. (a) False, y is not an exponential function of x.
( y can never be 0.)
0
5
−3
f x ln x, gx 4 x
10
f
g
g
f
12
(b) True, y could be log 2 x.
(c) True, x could be 2 y .
(d) False, y is not linear.
(The points are not collinear.)
© Houghton Mifflin Company. All rights reserved.
0
0
10,000
The rate of growth of the natural logarithmic
function is slower than for any n.
gx x 1n