Given the functions, compare their growth rates and order them from the fastest$-$

growing to the slowest$-$growing $(20$ points$)$:

$($a$)$

$f(n)=nlo{g}_2(n)$

$g(n)=n+n^2+n^3$

$h(n)=2^4$

$k(n)=\sqrt[\phantom{2}]{n}$

$($b$)$

$f(n)=n!$

$g(n)=2^n$

$h(n)=nlo{g}_2(n)$

$k(n)=lo{g}_2(n)$

$l(n)=n^3$