What is the largest input size n that can be solved in 50 ye

What is the largest input size n that can be solved in 50 years using an algorithm that takes t(n) =2ⁿ steps, on a computer that executes one step every one microsecond?

Solution

Micro is 10^(-6). 50yrs is 50*365*86400 seconds.

This is 15768*10^5 seconds. So this is equivalent to 15768*10^11 micro seconds.

As T(n) = 2n, so if time taken is 15768*10^11, then n is (15768/2)*10^11 which is 7884*10^11.