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

92. (a)
93.
(c)
200
7
140
V 4
3r 3 r 2 4r (b)
V 4
3r 3 4r 3
150
0
0
16
3 r 3
The model is a good fit to the actual data.
13
2
(d)
r ≥ 0
r 1.93 ft
Section 2.2 Polynomial Functions of Higher Degree 165
V 120 ft 3 16
3 r 3
length 4r 7.72 ft
y 1 0.139t 3 4.42t 2 51.1t 39 94.
95. Midwest:
97.
South:
y 218 $223.472 thousand $223,472
Since the models are both cubic functions with positive
leading coefficients, both will increase without bound
as t increases, thus should only be used for short term
projections.
(a)
y 0.056t 3 1.73t 2 23.8t 29
180
7
120
13
The data fit the model closely.
y 118 $259.368 thousand $259,368 96. Answers will vary.
G 0.003t 3 0.137t 2 0.458t 0.839,
60
−10 45
−5
(b) The tree is growing most rapidly at t 15.
102. (a) Degree: 3
Leading coefficient: Positive
(b) Degree: 2
Leading coefficient: Positive
2 ≤ t ≤ 34
(c)
Example: The median price of homes in the South are
all lower than those in the Midwest. The curves do
not intersect.
y 0.009t 2 0.274t 0.458
b 0.274
15.222
2a 20.009
y15.222 2.543
Vertex 15.22, 2.54
(d) The x-value of the vertex in part (c) is approximately
equal to the value found in part (b).
98. R
The point of diminishing returns (where the graph
changes from curving upward to curving downward)
occurs when x 200. The point is 200, 160 which
corresponds to spending $2,000,000 on advertising to
obtain a revenue of $160 million.
1
100,000x 3 600x2 99. False. A fifth degree polynomial can have at most four
turning points.
100. True. f x x 1 has one repeated solution.
6
(c) Degree: 4
Leading coefficient: Positive
(d) Degree: 5
Leading coefficient: Positive
101. True. A polynomial of degree 7 with a negative leading
coefficient rises to the left and falls to the right.