Question

CalculusThe Population of Logburgh grows by 4.3% each year. How long will it take for the population of Logburgh to double? Give your answer to the nearest tenth of a year.

Answer 1

Given data:

The given rate is r=4.3%.

The expression for the final population is,

$P=P_0e^{rt}$

Substitute the given values in the above expression.

$\begin{gathered} 2P_0=P_0e^{0.043t} \\ 2=e^{0.043t} \\ \ln 2=0.043t \\ t=16.119 \\ =16.1 \end{gathered}$

Thus, the value of time is 16.1 years.