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$($h$)2^{(\frac{5}{2})logn}=O(n^2)$

$2$ Recurrences $(32$ pts$)$

Solve the following recurrences, giving your answer in $$ notation $($so prove both an upper bound and a lower bound$).$ For each of them you may assume $T(x)=1$ for $x5.$ Justify your answer $($formal proof not necessary, but recommended$).$

$($a$)T(n)=5T(n-3)$

$($b$)T(n)=n^{\frac{1}{4}}T(n^{\frac{3}{4}})+n$

$($c$)T(n)=6T(\frac{n}{4})+n$

$($d$)T(n)=T(n-2)+10$

$1$