Question

Suppose the runtime of a computer program is proportional to the fourth root of the input size. If the original runtime is 165 ms and the input size is multiplied by 8,598 what is the new runtime in ms? (Just type the number not "ms"). Round your answer to the nearest whole number.

Answer 1

Lets assume, for convenience in calculations, that the original input size is 16 (it does not really matter what number you take the original input size to be, except for ease in calculating):

Input size of 16 ---> Fourth root of input size = 2 ------> Time = 165 ms

We now multiply the input size by 8598 to get 8598 x 16 = 137568. Fourth root of this number is 19.25881

Input size of 137568 ----> Fourth root of input size = 19.25881 -----> Time = 165 * 19.25881 / 2 = 1588.851 ms

Rounding off, we get time = 1589 ms.