Question

from 1956 to 1966 the number of automobiles in the country increased at an annual rate of 6.65 percent. what is the doubling time for growth in automobiles in the US?

Answer 1

A= P(1+i)ⁿ ,

where A is the value generated after a time " n" at an interest rate of i (in %).

When A = 2.P ?

Replace in the formula: 2.P = P(1+0.0665)ⁿ , after simplification by P, we get 

2= (1+0.0665)ⁿ

To calculate n, let' use ln (Neperian logarithm)
ln(2) = n.ln(1.0665) and

n=(ln2)/(ln(1.0665)  and  n=10.76 years ,