College Algebra 9th txtbk

Applications
One of the primary objectives of this book is to give the
student substantial experience in modeling and solving
real-world problems. Over 500 application exercises help
convince even the most skeptical student that mathematics
is relevant to everyday life. An Applications
Index is included following the features to help
locate particular applications.
15. 2 3 2 x 0.426 4.23 16. 3 4 3 x 0.089
6.20
In Problems 17–26, solve exactly.
17. log 5 x 2 x 25 18. log 3 y 4 y 81
19. log (t 4) 1 t 41
10 20. ln (2x 3) 0 x 1
21. log 5 log x 2 20 22. log x log 8 1 80
23. log x log (x 3) 1 5
24. log (x 9) log 100x 3 10
11
25. log (x 1) log (x 1) 1
9
26. log (2x 1) 1 log (x 2)
21
In Problems 27–34, solve to three significant digits.
27. 2 1.05 x 14.2 28. 3 1.06 x 18.9
29. e 1.4x 5 0 30. e 0.32x 0.47 0 No solution
No solution
31. 123 500e 0.12x 11.7 32. 438 200e 0.25x 3.14
33. e x2 0.23 1.21 34. e x2 125 2.20
B
In Problems 35–48, solve exactly.
35. log (5 2x) log (3x 1) 4
5
36. log (x 3) log (6 4x) 1
37. log x log 5 log 2 log (x 3) 5
2
38. log (6x 5) log 3 log 2 log x
3
39. ln x ln (2x 1) ln (x 2) 2 13
40. ln (x 1) ln (3x 1) ln x 1 12
1 189
41. log (2x 1) 1 log (x 1)
4
42. 1 log (x 2) log (3x 1) 3
43. ln (x 1) ln (3x 3) No solution
44. 1 ln (x 1) ln (x 1) No solution
8
54. L 8.8 5.1 log D for D (astronomy)
55. I E for t (circuitry)
R (1 eRtL )
56. S R (1 i)n 1
for n (annuity)
i
The following combinations of exponential functions define four
of six hyperbolic functions, a useful class of functions in calculus
and higher mathematics. Solve Problems 57–60 for x in terms of y.
The results are used to define inverse hyperbolic functions,
another useful class of functions in calculus and higher
mathematics.
57. 58. y e x e x
y e x e x
2
2
x ln(y
59. 60. y e x e x
y e x 2y 2
e x 1) x ln[y 2y 2 1]
e x e x
e x e x
x x 1 2 ln y 1
1 2 ln 1 y
1 y
y 1
In Problems 61–68, use a graphing calculator to approximate to
two decimal places any solutions of the equation in the interval
0 x 1. None of these equations can be solved exactly using
any step-by-step algebraic process.
61. 2 x 2x 0 0.38 62. 3 x 3x 0 x 0.25
63. e x x 0 0.57 64. xe 2x 1 0 x 0.43
65. ln x 2x 0 0.43 66. ln x x 2 0 x 0.65
67. ln x e x 0 0.27 68. ln x x 0 x 0.57
APPLICATIONS
D 10 (L8.8)5.1
t L RI
ln al
R E b
n ln(Si R 1)
ln(1 i )
69. COMPOUND INTEREST How many years, to the nearest year,
will it take a sum of money to double if it is invested at 7% compounded
annually? 10 years
70. COMPOUND INTEREST How many years, to the nearest year,
will it take money to quadruple if it is invested at 6% compounded
annually? 24 years
Technology Connections
Technology Connections boxes integrated at
appropriate points in the text illustrate how concepts
previously introduced in an algebraic context
may be approached using a graphing
calculator. Students always learn the algebraic
methods first so that they develop a solid grasp
of these methods and do not become calculatordependent.
The exercise sets contain calculatorbased
exercises that are clearly marked with a
calculator icon. The use of technology is
completely optional with this text. All technology
features and exercises may be omitted without sacrificing
content coverage.
Technology Connections
Figure 1 shows the details of constructing the logarithmic model of Example 5 on a graphing calculator.
0
(a) Entering the data (b) Finding the model (c) Graphing the data and the model
Z Figure 1
0
100
62. g(x) 4e x1 7; f(x) e x
63. g(x) 3 4e 2x ; f(x) e x
64. g(x) 2 5e 4x ; f(x) e x
In Problems 65–68, simplify.
2x 3 e 2x 3x 2 e 2x
5x 4 e 5x 4x 3 e 5x
65. 66.
x 6
x 8
67. (e x e x ) 2 (e x e x ) 2 2e 2x 2e 2x
68. e x (e x 1) e x (e x 1) e x e x
120
In Problems 69–76, use a graphing calculator to find local
extrema, y intercepts, and x intercepts. Investigate the behavior as
x S and as x and identify any horizontal asymptotes.
Round any approximate values to two decimal places.
69. f(x) 2 e x2 70. g(x) 3 e 1x
71. s(x) e x2
72. r(x) e x2
xviii