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

72. (a) x-intercepts:
(b) 0 x 3 2
1, 0, 2, 0 73. C
x
(a) 2,000
255p
, 0 ≤ p < 100
100 p
74. C
(a) 300,000
25,000p
, 0 ≤ p < 100
100 p
75.
205 3t
N , t ≥ 0
1 0.04t
(a) N5 333 deer
(b)
76. (a)
0 x 2 3x 2
0 x 1x 2
x 1, x 2
0
0
C
The cost would be $4411.76.
25,00015
4411.76
100 15
C 25,00050
100 50
100
25,000
The cost would be $25,000.
C
The cost would be $225,000.
(c) C → as x → 100. No. The model is undefined for
p 100.
25,00090
225,000
100 90
0.2550 0.75x C50 x (c)
C
C
(b) Domain:
12.50 0.75x
50 x
4
4
50 3x 3x 50
450 x 4x 50
x ≥ 0 and x ≤ 1000 50
Thus, 0 ≤ x ≤ 950. Using interval notation, the
domain is 0, 950.
(b)
0
0
Section 2.6 Rational Functions 219
C10 25510
28.33 million dollars
100 10
C40 25540
170 million dollars
100 40
C75 25575
765 million dollars
100 75
(c) C → as x → 100. No, it would not be possible
to remove 100% of the pollutants.
N10 500 deer
N25 800 deer
(b) The herd is limited by the horizontal asymptote:
N 60
1500 deer
0.04
1.0
0.8
0.6
0.4
0.2
C
100
200 400 600 800 1000
(d) As the tank is filled, the concentration increases
more slowly. It approaches the horizontal asymptote
of C 3
4 0.75.
x