Question

A population of 10,000 is increasing by 6% each year, how many years until the population will double?

Answer 1

Hello

Since we are looking for the time it takes for the population to be doubled, we can use this formula

`\begin{gathered} A=p(1+(r)/(100))^n \\ A=20000 \\ p=10000 \\ r=6 \\ 20000=10000(1+(6)/(100))^n \\ (20000)/(10000)=(1+0.06)^n \\ 2=1.06^n \end{gathered}`

To solve for n, we would take log of both sides

`\begin{gathered} 2=1.06^n \\ \log 2=n\log 1.06 \\ n=(\log 2)/(\log 1.06) \\ n=11.89\approx12 \end{gathered}`

It would take approximately 12 years to double the population