Answer
$f(x)= \left(\frac{1}{2} \right)^x$
Work Step by Step
27)Let $f(x)=a b^x$. We know from the graph that $f(0)=a b^0= a=1$ and $f(4)= b^{4}=\frac{1}{16}$. So
$$
\begin{aligned}
(1) b^2 & = \frac{1}{16}\\
b & =\left(\frac{1}{2^4}\right)^{\frac{1}{4}} \\
b=\frac{1}{2} & \text { or } b=-\frac{1}{2}
\end{aligned}
$$ Hence
$f(x)= \left(\frac{1}{2} \right)^x$
