We have the recurrence relation $T(n)=7T(\frac{n}{2})+100n^{lo{g}_{2}7}.$ Suppose that we

want to use the Master method to solve $T(n).$ We need to decide the case and derive the

conclusion. In the dropdown lists, $\backslash$Theta stands for $\frac{,}{\mathit{l}\mathit{o}\mathit{g}}\_$ b a stands for $lo{g}_{b}a,$ and $n^{{?}^{{?}^{?}}}x$

stands for $n^x.$

$($a$)$ Which case of the Master method this recurrence falls into?

$($b$)$ What is the asymptotic notation of $T(n)?$