Question

Question Part
Points
Submissions Used
A model for the population in a small community after t years is given by the equation
P(t) = P0ekt, k > 0.
(a) If the initial population has doubled in 5 years, how long will it take to triple? (Round your answer to two decimal places.)
yr

If the initial population has doubled in 5 years, how long will it take to quadruple? (Round your answer to the nearest integer.)
yr

(b) If the population of the community in part (a) is 10,000 after 3 years, what was the initial population? (Round your answer to the nearest integer.)
P0 =

Answer 1

Part A:
\[\frac{P(5)}{P_o} = 2 = e^{5k} \rightarrow \ln(2) = 5k \rightarrow k = \frac{\ln(2)}{5} \approx 0.1386\]
\[P(t) = P_oe^{0.1386t}\]
so to find the time to triple,
\[\frac{P(t)}{P_o} = 3 = e^{0.1386t} \rightarrow \ln(3) = 0.1386t \rightarrow t = 7.92 years\]
\[\frac{P(t)}{P_o} = 4 = e^{0.1386t} \rightarrow \ln(4) = 0.1386t \rightarrow t = 10 years\]
Part B:
\[P_o = P(t)e^{-0.1386t} = 10,000e^{-0.1386*3} = 6,598\]

Answer 2

THANKS!