Problem $10$: Recurrences

$[$a$]$ Use the Master Theorem to determine the order of magnitude of T$($n$)=8$T$($n$/2)+$ n for n $>1,$ where T$(1)=1.$

$[$b$]$ State the characteristic equation of the recurrence S$($n$)=9$S$($n$-1)-8$S$($n$-2)$ for n $>1,$ where S$(0)=6$ and S$(1)=7.$

$[$c$]$ Using the methods of our course, derive a closed$-$form formula for either S$($n$)$ or T$($n$)$