$12\mathrm{.}9\mathrm{.}3$: Calculating the asymptotic growth rate $-$ step by step.

help$\_$outline

Consider the recurrence relation T$($n$)=5$T$($n$2)+3$n$3.$ Assume that n is a power of $2,$ that is$,$ n$=2$k for some integer k$.$

$($a$)$

If the levels of an expansion of the recurrence relation are numbered $0$ through L$,$ then what is the value of L$?$ Express your answer in terms of n$.$

$($b$)$

If the levels of an expansion of the recurrence relation are numbered $0$ through L$,$ then how many terms are there at level j$?$

$($c$)$