Many years ago, the towns of Franklin and Chester agreed to begin posting their populations on signs just outside of their towns. They also agreed to update their signs once per year at the beginning of the year.
During year
1
11, Franklin's sign read "
Franklin: Population of
20
,
000
Franklin: Population of 20,000start text, F, r, a, n, k, l, i, n, colon, space, P, o, p, u, l, a, t, i, o, n, space, o, f, space, end text, 20, comma, 000", while Chester's sign read "
Chester: Population of
25
,
000
Chester: Population of 25,000start text, C, h, e, s, t, e, r, colon, space, P, o, p, u, l, a, t, i, o, n, space, o, f, space, end text, 25, comma, 000". Each year, the populations grew. Specifically, Franklin's population grew by
5
%
5%5, percent each year, and Chester's population grew by
500
500500 people each year.
What is the first year in which Franklin's sign shows a larger number than Chester's sign?