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

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

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

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