For the next few questions, consider defining a time function with respect to n$.$ That is$,$ if

the algorithm is linear, we could write the time that it takes as a function of n:

t $=$ f$($n$)=$ cn

If it is quadratic, we could write it as a quadratic function:

t $=$ f$($n$)=$ cn$2$

Both of these instances ignore lower order terms. If we know the time it takes for a particular

value of n then we can compute the constant c and consequently predict the time t it takes

for other values of n or vice versa.

$3.5$ points An algorithm takes $4\mathrm{.}5$ ms for an input size $100.$ How long will it take for

input size $2000($assuming that low$-$order terms are negligible$)$ if the running time is

$($a$)$ linear

$($b$)$ O$($n log n$)$

$($c$)$ quadratic

$($d$)$ cubic

$($e$)$ exponential