Answer
$f(x)=\left(\dfrac{1}{4}\right)^x$
Work Step by Step
Substituting $x=
2
$ and $f(x)=
\dfrac{1}{16}
$ in the given function, $f(x)=a^x$, then the value of $a$ is
\begin{array}{l}\require{cancel}
\dfrac{1}{16}=a^{2}
\\\\
a=\pm\sqrt{\dfrac{1}{16}}
\\\\
a=\pm\dfrac{1}{4}
.\end{array}
Since the base of an exponential function is nonnegative, then $a=\dfrac{1}{4}.$ Hence, the equation of the given graph is $
f(x)=\left(\dfrac{1}{4}\right)^x
.$
