[tex]\bf \stackrel{\textit{started, t = 0, A = 5000}}{\qquad \textit{Amount for Exponential Growth}}
\\\\
A=P(1 + r)^t\qquad
\begin{cases}
A=\textit{accumulated amount}\to &5000\\
P=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &0\\
\end{cases}
\\\\\\
5000=P(1+r)^0\implies \boxed{5000=P}\\\\
-------------------------------[/tex]
[tex]\bf \stackrel{\textit{2 hours later, t = 2, A = 5500}}{\qquad \textit{Amount for Exponential Growth}}
\\\\
A=P(1 + r)^t\qquad
\begin{cases}
A=\textit{accumulated amount}\to &5500\\
P=\textit{initial amount}\to &5000\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &2\\
\end{cases}[/tex]
[tex]\bf 5500=5000(1+r)^2\implies \cfrac{5500}{5000}=(1+r)^2\implies \cfrac{11}{10}=(1+r)^2
\\\\\\
\sqrt{\cfrac{11}{10}}=1+r\implies \sqrt{\cfrac{11}{10}}-1=r\implies 0.0488\approx r\\\\
-------------------------------\\\\
\boxed{A\approx 5000(1+0.0488)^t}\qquad \qquad \stackrel{\textit{after 10 hours, t = 10}}{A\approx 5000(1.0488)^{10}}
\\\\\\
A\approx 8051.87[/tex]
