A certain algorithm takes 10^-4 times 2^n 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 times n^3 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 instances of size than 20