Question

The current (2015) population of Eugene is approximately 155,000 people. a) If the population growth rate remains at 4% per year, approximately when will the city of Eugene have 500,000 people? The current (2015) population of Eugene is approximately 155,000 people.

Answer 1

`\bf \textit{Amount of Population Growth}\\\\ A=Ie^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\to &500,000\\ I=\textit{initial amount}\to &155,000\\ r=rate\to 4\%\to (4)/(100)\to &0.04\\ t=\textit{elapsed time}\\ \end{cases}`


`\bf 500000=155000e^(0.04t)\implies \cfrac{500000}{155000}=e^(0.04t)\implies \cfrac{100}{31}=e^(0.04t) \\\\\\ \textit{now, we take \underline{ln} to both sides} \\\\\\ ln\left( (100)/(31)\right)=ln(e^(0.04t))\implies ln\left( (100)/(31)\right)=0.04t\implies \cfrac{ln\left( (100)/(31)\right)}{0.04}=t`

so it will have 500,000 approximately "t" years after 2015.