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?

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