Question

Joey saved $2 today. if he doubles the number of dollars he saves each day, how many days, including today, will it take him to save more than $500?

Answer 1

as the days go by:
1*2
2*2
4*2 by the third day, Joey has (2^2)*2 dollars
8*2 by the 4th day, Joey has (2^3)*2 dollars
16*2 by the 5th day, Joey has (2^4)*2 dollars
so by the nth day, he has 2^(n-1)*2, which is 2^n
2^n>500
n is about 9