A certain algorithm takes 10-4 * 2n seconds to solve an instance of size n. Show

Question

A certain algorithm takes 10-4 * 2n seconds to solve an instance of size n. Show that in a year it could just solve an instance of size 38. What size of instance could be solved in a year on a machine one hundred times as fast? A second algorithm takes 10-2 * n3 seconds to solve an instance of size n. What size instance can it solve in a year? What size instance could be solved in a year on a machine one hundred times as fast? Show that the second algorithm is nevertheless slower than the first for instance of size less than 20.

Explanation / Answer

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