If a program takes 4 microseconds to process a list of 10 numbers. How long would you expect it to take to process a list of 100 numbers? Answer the question in the different scenarios below, where T(n) represents the runtime as a function of n, the list size and k is a constant. Justify your answer using one or more of the rules of thumb we discussed. Express the answer in appropriate units whenever it's bigger than 1000 microseconds (e.g. milliseconds, seconds, minutes, days, months, years). k is a constant.

a)T(n) = k

b) T(n) = k (logn)

c) T(n) = k (sqrt(n))

d) T(n) = kn

e) T(n) = k nlogn

f) T(n) = k (n2)

i) T(n) = k (2n) please show work as well! Thank you!