Question $2()$:

Suppose the exact time required for an algorithm $A$ in both the best and worst cases is given by the

function

$T_A(n)=\frac{1}{280}{n}^2+42logn+12n^3+280\sqrt[\phantom{2}]{n}$

$($a$)(2$ points$)$ For each of the following statements, indicate whether the statement is true or false.

Algorithm A is $O(logn)$

Algoirthm $A$ is $O(n^2)$

Algoirthm A is $O(n^3)$

Algoirthm A is $O(2^n)$

$($b$)(1$ point$)$ Can the time complexity of this algorithm be expressed using big$-$ notation? If so$,$

what is it$?$