Page 182 - How To Solve Word Problems In Calculus

rt
7. After t years P dollars will be worth an amount A = Pe .We
would like to determine the value of t when A = 3P .
A = Pe rt
3P = Pe 0.1t

3 = e 0.1t

0.1t = ln 3
ln 3 1.0986
t = ≈ = 10.986
0.1 0.1
It will take almost 11 years for the money to triple.
rt
8. A = Pe . In this problem, A = 8000 and we wish to find P . The
1
value of r = 0.05 and t = year.
2
A = Pe rt

1
(0.05)( 2 )
8000 = Pe
0.025
8000 = Pe
P = 8000e −0.025

= 8000 × 0.9753
≈ $7802.48
5000
9. P (t) = .
1 + 4e −0.4t
(a) The number of fish initially placed into the lake is the population
at time t = 0.
5000 5000
P (0) = = = 1000 fish
1 + 4e −(0.4)(0) 1 + 4

(b) The population of fish after 5 months is P (5).
5000 5000
P (5) = =
1 + 4e −(0.4)(5) 1 + 4e −2
5000
= ≈ 3244 fish
1 + 4(0.135335)

(c) The population growth rate is the derivative of the population
function P (t).
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