Answer
$f(x)= 2\cdot\left(0.80\right)^x$
Work Step by Step
Let $f(x)=a b^x$. We know from the graph that $f(-1)=a b^{-1}=2.5$ and $f(1)=a b^{1}=1.6$. So
$$
\begin{aligned}
\frac{a b^1}{a b^{-1}} & =\frac{1.6}{2.5} \\
b^2 & =0.64 \\
b & =0.8 = \frac{4}{5}
\end{aligned}
$$ and $$
\begin{aligned}
& a b^{-1}=2.5 \\
& a=b\cdot 2.5 \\
&=0.8\cdot 2.5 \\
& =2.
\end{aligned}
$$ Hence $$f(x)= 2\cdot\left(0.80\right)^x$$
