Answer
$
f(x)=-3\cdot\left(\frac{1}{2}\right)^x
$
Work Step by Step
We want to find $f(x)=ab^x$,given $f(3)=-3 / 8$ and $f(-2)=-12$. We now find $b$ and $a$.
$$
\begin{aligned}
\frac{ab^3}{ab^{-2}}& =\frac{f(3)}{f(-2)} \\
b^5 & =\frac{-3/8}{-12}\\
b & =\left(\frac{1}{32}\right)^{1/5}=\frac{1}{2}
\end{aligned}
$$ and $$
\begin{aligned}
ab^{-2} & =-12 \\
a & =-12b^2 \\
a& =-12\cdot\frac{1}{4} =- 3.
\end{aligned}
$$ Hence $$
f(x)=-3\cdot\left(\frac{1}{2}\right)^x
$$
