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200 Chapter 3 Exponential and Logarithmic Functions
50.
15,000
51.
fx x 2 e x
(a)
7
0 600
0
Intersection: 482.831, 12,500
−3
−1
(b) Decreasing:
9
, 0, 2,
52.
(b) Increasing on and
(a)
, 2 0,
f x 2x 2 e x1 Decreasing on 2, 0
10
−13
5
−2
(c) Relative maximum: 2, 2.943
Relative minimum: 0, 0
Increasing: 0, 2
(c) Relative maximum: 2, 4e 2 2, 0.541
Relative minimum: 0, 0
53.
P 2500, r 2.5% 0.025, t 10
Compounded n times per year:
A P 1
n r nt 2500 1 0.025
n 10n
Compounded continuously: A Pe rt 2500e 0.02510
n 1 2 4 12 365 Continuous
A 3200.21 3205.09 3207.57 3209.23 3210.04 3210.06
54. P 1000, r 6% 0.06, t 10
n 1 2 4 12 365 Continuous
A 1790.85 1806.11 1814.02 1819.40 1822.03 1822.12
55.
P 2500, r 4% 0.04, t 20
Compounded n times per year:
A P 1 r n nt 2500 1 0.04
n 20n
Compounded continuously: A Pe rt 2500e 0.0420
n 1 2 4 12 365 Continuous
A 5477.81 5520.10 5541.79 5556.46 5563.61 5563.85
56. P 1000, r 3% 0.03, t 40
n 1 2 4 12 365 Continuous
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A 3262.04 3290.66 3305.28 3315.15 3319.95 3320.12