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EPPDISCMATH$511\mathrm{.}3\mathrm{.}005.$

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

Suppose that when run with an input of size $n,$ algorithm A requires ${10}^6{n}^4$ operations and algorithm $B$ requires $n^5$ operations.

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

algorithm A order $n$

algorithm $B$ order $n$

$($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 B at least $100$ times more efficient than algorithm A$?($Enter your answer as a single inequality solved for $n.)$

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