Answer
$y=4\left(3^{x}\right)$
Work Step by Step
The exponential function we want has the form $y=Ab^{x}$.
$\left[\begin{array}{ll}
\text{point on} & \text{corresponding}\\
\text{the graph} & \text{equation}\\\\
(2,36) & 36=Ab^{2}\\
(4,324) & 324=Ab^{4}
\end{array}\right]$
Dividing the equations,
$\displaystyle \frac{324}{36}=\frac{Ab^{4}}{Ab^{2}}$
$9=b^{2}$,
$b=3.$
Back-substituting into the first equation,
$36=A(3)^{2}$
$36=9A$
$A=4$
The model is
$y=Ab^{x}=4\left(3^{x}\right)$
