Estimate 3^100

Problem: estimate the value of 3^100.

Solution: A so called "72" rule will be used. The rule states if the percentage of annual GDP increase is a, it takes 72/a years to double the GDP. So 3^100 = 9^50 = 10^50/1.1^50 = 10^50/(1.1*1.1^(7*7)) = 10^50/(1.1*2^7) = 10^50/140 = 1000/140 *10^47 = 7*10^47. Another way is to leverage 3^9 = 20000.