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)=(1,395,000)/(775,000) \\ e^(0.0675t)=1.8 \\ \ln (e^(0.0675t))=\ln (1.8) \\ 0.0675t=\ln (1.8) \\ t=(\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.