Question

The population of Boom town is 775,000 and is increasing at a rate of 6.75% each year. How many years will it take to reach a population of 1,395,000?

Answer 1

To study population growth, we use the following formula

$P=P_0\cdot e^{rt}$

Where,

$\begin{gathered} P=1,395,000 \\ P_0=775,000 \\ r=0.0675 \end{gathered}$

Let's replace the values above, and solve for t.

$\begin{gathered} 1,395,000=775,000\cdot e^{0.0675t} \\ e^{0.0675t}=\frac{1,395,000}{775,000} \\ e^{0.0675t}=1.8 \\ \ln (e^{0.0675t})=\ln (1.8) \\ 0.0675t=\ln (1.8) \\ t=\frac{\ln (1.8)}{0.0675} \\ t\approx8.7 \end{gathered}$

Hence, it would take 8.7 years to reach a population of 1,395,000.