Use the iteration method to solve the recurrence, T$($n$)=4$T$($n$/2)+$ n$,$ T$(4)=6.$Problem $5.$

Rank the following functions by order of growth; that is$,$ find an arrangement $g_1,g_2,g_3,$dots,$g_6$ of the functions

satisfying $g_1=(g_2),g_2=(g_3),g_3=(g_4),g_4=(g_5),g_5=(g_6).$ Partition your list in equivalence

classes such that $f(n)$ and $h(n)$ are in the same class if and only if $f(n)=(h(n)).$ For example for functions

$lgn,n,n^2,$ and $2^{lgn}$ you could write: $,n^2,\{n,2^{lgn}\},lgn.$

$2^n,3^{lgn},2^{3lgn},n^{2}lgn,lg(n!),n!$