Answer
$n=12$
Work Step by Step
$a_n=2048\left(\frac{1}{2}\right)^n-80$ when $a_n=-79.5$
$2048\left(\frac{1}{2}\right)^n-80=-79.5$
$\implies 2048\left(\frac{1}{2}\right)^n=0.5$
$\implies\left(\frac{1}{2}\right)^n=\frac{1}{4096}$
$\implies n=\log_{\frac{1}{2}}\frac{1}{4096}=12$