Answer
$y=4\left(0.3^{x}\right)$
Work Step by Step
The exponential function we want has the form $y=Ab^{x}$.
$\left[\begin{array}{ll}
\text{point on} & \text{corresponding}\\
\text{the graph} & \text{equation}\\
(1,1.2) & 1.2=Ab^{1}\\
(3,-0.108) & 0.108=Ab^{3}
\end{array}\right]$
Dividing the equations,
$\displaystyle \frac{0.108}{1.2}=\frac{Ab^{3}}{Ab^{1}}$
$0.09=b^{2}$, so
$b=0.3$
Back-substituting into the second equation,
$1.2=A(0.3)^{1}$
$A=\displaystyle \frac{1.2}{0.3}=4$
The model is
$y=Ab^{x}=4\left(0.3^{x}\right)$
