Answer
$y=-1\left(0.2^{x}\right)$
Work Step by Step
The exponential function we want has the form $y=Ab^{x}$.
$\left[\begin{array}{ll}
\text{point on} & \text{corresponding}\\
\text{the graph} & \text{equation}\\
(-2,-25) & -25=Ab^{-2}\\
(1,-0.2) & -0.2=Ab^{1}
\end{array}\right]$
Dividing the equations,
$\displaystyle \frac{-0.2}{-25}=\frac{Ab^{1}}{Ab^{-2}}$
$0.008=b^{1-(-2)}$, so
$b^{3}=0.008$
$b=0.2$
Back-substituting into the second equation,
$-0.02=A(0.2)^{1}$
$A=\displaystyle \frac{-0.02}{0.2}=-1$
The model is
$y=Ab^{x}=-1\left(0.2^{x}\right)$
