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202 Chapter 3 Exponential and Logarithmic Functions
66. (a)
y 1 5001 0.07 x 67.
y 2 500 1 0.07
4 4x
y 3 500e 0.07x
2000
y 2
y 3
y 1
Q 25 1 2 t1599
(a) When t 0,
Q 25 1 2 01599 251 25 grams.
(b) When t 1000,
Q 25 1 2 10001599 16.21 grams.
(c)
30
(b)
0
20
0
y 3
has the highest return.
After 20 years,
y 2 y 1 2003.20 1934.84 $68.36
y 3 y 2 2027.60 2003.20 $24.40
y 3 y 1 2027.60 1934.84 $92.76
0
0
5000
(d) Never. The graph has a horizontal
asymptote Q 0.
68.
Q 10 1 2 t5715 69.
Pt 100e 0.2197t
(a) When t 0, Q 10.
(b) When t 2000,
(a)
2000
Q 10 1 2 20005715 7.85 grams.
(c)
Q
0
0
15
Mass of 14 C (in grams)
12
10
8
6
4
2
4000 8000
Time (in years)
t
(b)
(c)
P0 100
P5 300
P10 900
P0 100e 0.21970 100
P5 100e 0.21975 299.966 300
P10 100e 0.219710 899.798 900
70. (a) 50
(b)
(c)
15 30
30
P 34.706e 0.0097t 50
e 0.0097t 1.441
(Answers will vary.)
0.0097t ln1.441
t 38, or 2038
Year 2015 2016 2017 2018 2019 2020 2021 2022
P 40.1 40.5 40.9 41.3 41.7 42.1 42.5 43.0
Year 2023 2024 2025 2026 2027 2028 2029 2030
P 43.4 43.8 44.2 44.7 45.1 45.5 46.0 46.4
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