For relatively small valaes of $n,$ algorithms with largar orders can be more efficient than algorithms with smaller orders.

Suppose that when run with an input of size $n,$ algorithm A requires ${10}^6{n}^3$ operations and algorithm $B$ requires $n^4$ operations.

$($a$)$ What are orders for algorithms A and $B$ from among the set of power functions?

algarithm A order

algocithm B$.$ order

$($b$)$ For what values of $n$ is algorithm A more efficient than algorithm $B?($Enter your answer as a single inequality solved for $n.)$

$($c$)$ for what values of $n$ is algorithm is at least $100$ times more efricient than algorithm $A?($Enter your answer as a single inequality solved fur $n.)x$

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