Answer
$f(x)= 5\cdot\left(\frac{2}{3}\right)^x$
Work Step by Step
Let $f(x)=a b^x$. We know from the graph that $f(-2)=a b^{-2}=\frac{45}{4}$ and $f(1)=a b^{1}=\frac{10}{3}$. So
$$
\begin{aligned}
\frac{a b^1}{a b^{-2}} & =\frac{10/3}{45/4} \\
b^3 & =\frac{8}{27} \\
b & =\frac{2}{3}
\end{aligned}
$$
and
$$
\begin{aligned}
& a b^{-2}=\frac{45}{4} \\
& a=b^2\cdot \frac{45}{4} \\
&=\frac{4}{9}\cdot \frac{45}{4} \\
& =5.
\end{aligned}
$$ Hence $$f(x)= 5\cdot\left(\frac{2}{3}\right)^x$$
