C H A P T E R 2 Polynomial and Rational Functions

73.
C 0.0031t 3 0.216t 2 5.54t 19.1, 0 ≤ t ≤ 23
(a)
74. (a)
80
0 23
0
(b)
t C
C will be greater than 75% when
t 31, which corresponds to 2011.
24 70.5
26 71.6
28 72.9
30 74.6
32 76.8
34 79.6
(c) C 75 when t 30.41.
(b)
76. (a)
(c)
Maximum safe load
d 4 6 8 10 12
Load 2223.9 5593.9 10,312 16,378 23,792
25,000
20,000
15,000
10,000
5,000
L
2000 ≤ 168.5d 2 472.1
2472.1 ≤ 168.5d 2
14.67 ≤ d 2
3.83 ≤ d
4 6 8 10 12
Depth of the beam
The minimum depth is 3.83 inches.
d
Section 2.7 Nonlinear Inequalities 235
(d)
t C
C will be between 85% and 100%
when t is between 37 and 42. These
36 83.2 values correspond to the years 2017 to
2022.
37 85.4
38 87.8
39 90.5
40 93.5
41 96.8
42 100.4
43 104.4
(e) 85 ≤ C ≤ 100 when 36.82 ≤ t ≤ 41.89 or 37 ≤ t ≤ 42.
(f) The model is a third-degree polynomial and as
t →, C →.
75.
2R 1
R
2 R1 N 0.03t 2 9.6t 172 (b) and (d)
220 ⇒ t 5
So the number of master’s degrees earned by women
exceeded 220,000 in 1995.
N 0.03t 2 9.6t 172
320 ⇒ t 16.2
So the number of master’s degrees earned by women
will exceed 320,000 in 2006.
1 1
R R1 1
2
2R 1 2R RR 1
2R 1 R2 R 1
Since R ≥ 1, we have
2R 1
1 ≥ 0
2 R1 R 1
2R 1
≥ 1
2 R1 2
≥ 0.
2 R1 Since R1 > 0, the only critical number is R1 2. The
inequality is satisfied when R 1 ≥ 2 ohms.
Master's degrees earned
(in thousands)
320
280
240
200
160
N
2 6 10 14 18
Year (0 ↔ 1990)
N = 320
N = 220
t