Question

The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 3 years, how long will it take to triple? (Round your answer to one decimal place.)

Answer 1

4.75 years are required to triple the population

Explanation:

As we know

`(dP)/(dt) = P\\`

Integrating both the side with respect to t we get

`ln P = kt + c_1\\P = e^(kt + c_1)\\P = Ce^(kt)`

At t = 0, P = P0

`2 P_0 = P_0 * e ^(3k)\\2 = e ^(3k)\\ln 2 = 3k\\k = 0.231\\`

substituting K value in main equation, we get -

`P = P_0 * e^(0.231 * t)\\3P_0 = P_0 * e^(0.231 * t)\\3 = e^(0.231 * t)\\ln 3 = 0.231 * t\\t = 4.75`

4.75 years are required to triple the population