Answer
$y=3.6742\left(0.9036^{x}\right)$
Work Step by Step
The exponential function we want has the form $y=Ab^{x}$.
$\left[\begin{array}{ll}
\text{point on} & \text{corresponding}\\
\text{the graph} & \text{equation}\\
(2,3) & 3=Ab^{2}\\
(6,2) & 2=Ab^{6}
\end{array}\right]$
Dividing the equations,
$\displaystyle \frac{2}{3}=\frac{Ab^{6}}{Ab^{2}}$
$\displaystyle \frac{2}{3}=b^{4}$, so
$b=\displaystyle \left(\frac{2}{3}\right)^{1/4}\approx 0.9036$
Back-substituting into the second equation,
$3=A(0.9036)^{2}$
$A=\displaystyle \frac{3}{(0.9036)^{2}}\approx 3.6742$
The model is
$y=Ab^{x}=3.6742\left(0.9036^{x}\right)$
$y=3.6742\left(0.9036^{x}\right)$