if the population is doubling every 10 years, the rate of change is 100%, for the period of 10 years, so, whatever it happens to be at the time, it grows by 100%, namely it doubles.
[tex]\bf \textit{Periodic Exponential Growth}\\\\
A=I(1 + r)^{\frac{t}{p}}\qquad
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\to &4100\\
r=rate\to 100\%\to \frac{100}{100}\to &1.00\\
t=\textit{elapsed time}\to &8\\
p=period\to &10
\end{cases}
\\\\\\
A=4100(1 + 1)^{\frac{8}{10}}\implies A=4100(2)^{\frac{4}{5}}\implies A=4100\sqrt[5]{2^4}[/tex]
