Answer
$y=1.6818\left(0.8409^{x}\right)$
Work Step by Step
The exponential function we want has the form $y=Ab^{x}$.
$\left[\begin{array}{ll}
\text{point on} & \text{corresponding}\\
\text{the graph} & \text{equation}\\
(-1,2) & 2=Ab^{-1}\\
(3,1) & 1=Ab^{3}
\end{array}\right]$
Dividing the equations,
$\displaystyle \frac{1}{2}=\frac{Ab^{3}}{Ab^{-1}}$
$\displaystyle \frac{1}{2}=b^{4}$, so
$b=\displaystyle \left(\frac{1}{2}\right)^{1/4}\approx 0.8409$
Back-substituting into the second equation,
$2=A(0.8409)^{-1}$
$A=2(0.8409)=1.6818$
The model is
$y=Ab^{x}=1.6818\left(0.8409^{x}\right.$
$y=1.6818\left(0.8409^{x}\right)$
