$(16$ pts$)$ Determine the asymptotic growth of the following functions using big $O$ notation. You do not

need to find values of $c$ and no$.$

$($a$)f(n)=80\sqrt[\phantom{2}]{n}-{11}^{23}lo{g}_7(n)$

Asymptotic growth in terms of big $O$ notation $(4$ pts$)$:

$($b$)f(n)=(\frac{2}{33}{)}^{n+1}+2n^{12}+101n!$

Asymptotic growth in terms of big $O$ notation $(4$ pts$)$:

$($c$)f(n)=\frac{3}{256}{n}^{5}log(n^{22})$

Asymptotic growth in terms of big $O$ notation $(4$ pts$)$:

$($d$)f(n)=2^{5n}+{12}^6$

Asymptotic growth in terms of big O notation $(4$ pts$)$: