$(10$ points$)$ Assume that each of the expressions below gives the processing time $T(n)$ spent by an

algorithm for solving a problem of size $n.$

Express the asymptotic time complexity for each algorithm in terms of "big$-0"$ notation. You

should use master method for handling recurrence relations $($show your work$)$

For each pairs of algorithms, indicate whether the first algorithm has a lower, same, or higher

order of growth than the second algorithm. Justify your answer.

$T(n)=10T(\frac{n}{10})+n^2$

and

$T(n)=100T(\frac{n}{10})+n^2$

$T(n)=5T(\frac{n}{2})+n$

$T(n)=100n+4$

$T(n)=2^{2n-2}$

$T(n)=n^{4}log(n)$

and

$T(n)=9T(\frac{n}{3})+n^2$

and

and

and

$T(n)=lo{g}_2{2}^{(3n+2)}$

$T(n)=2^{2n+1}$

$T(n)=2^{10}+n^{4}log(n^3)-100n^4$