An algorithm takes $0\mathrm{.}5$ ms for input size $100.$ How long will it take for input size $500$ if the

running

time is the following $($assume low$-$order terms are negligible$)?$

$($a$)$ linear

$($b$)O(NlogN)$

$($c$)$ quadratic

$($d$)$ cubic

Select one or more:

a$.($a$)$ five times as long, or $2\mathrm{.}5$ ms

b$.($d$)12$ times as long, or $6$ ms

c$.($a$)10$ times as long, or $25$ ms $,$

d$.($c$)25$ times as long, or $12\mathrm{.}5$ ms

e$.($d$)125$ times as long, or $62\mathrm{.}5$ ms

f$.($b$)$ slightly more than five times as long