Hello
Since we are looking for the time it takes for the population to be doubled, we can use this formula
[tex]\begin{gathered} A=p(1+\frac{r}{100})^n \\ A=20000 \\ p=10000 \\ r=6 \\ 20000=10000(1+\frac{6}{100})^n \\ \frac{20000}{10000}=(1+0.06)^n \\ 2=1.06^n \end{gathered}[/tex]To solve for n, we would take log of both sides
[tex]\begin{gathered} 2=1.06^n \\ \log 2=n\log 1.06 \\ n=\frac{\log 2}{\log 1.06} \\ n=11.89\approx12 \end{gathered}[/tex]It would take approximately 12 years to double the population
