[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad
\begin{cases}
A=\textit{accumulated amount}\to &2090\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &0\\
\end{cases}
\\\\\\
2090=I(1+r)^0\implies 2090=I\\\\
-------------------------------\\\\[/tex]
[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad
\begin{cases}
A=\textit{accumulated amount}\to &3849\\
I=\textit{initial amount}\to &2090\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &\stackrel{2000-2005}{5}\\
\end{cases}[/tex]
[tex]\bf 3849=2090(1+r)^5\implies \cfrac{3849}{2090}=(1+r)^5\implies \sqrt[5]{\cfrac{3849}{2090}}=1+r
\\\\\\
\sqrt[5]{\cfrac{3849}{2090}}-1=r\implies 0.129900823\approx r\implies 0.13\approx r\\\\
-------------------------------\\\\
A=2090(1+0.13)^t\implies \boxed{A=2090(1.13)^t}[/tex]
