Find the value of k in the following so that the function $f$ is continuous at the indicated point: $f(x)=\left \{\begin{array}{1 1}\frac{\large 2^{x+2}-16}{4^{\large x}-16}, & if\;x\neq 2\\k, & if\;x=2\end{array}\right.$ at $x=2$

Question

$\begin{array}{1 1} k=\frac{1}{2} \\k= \frac{1}{4} \\ k=2 \\ k=4 \end{array}$