I was doing some extra khan academy when I stumbled across this question:

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 11, Franklin's sign read "Franklin: Population 20,000", while Chester's sign read "Chester: Population 25,000". Each year, the populations grew. Specifically, Franklin's population grew by 5% each year, and Chester's population grew by 500 people each year. What is the first year in which Franklin's sign shows a larger number than Chester's sign?

I made these two equations:

20,000 * (1.05)^t

25,000 + 500 * t

I eventually found that the answer was 9 by just repeatedly plugging in numbers with t, but it took me about 45 min to figure out. If you have a faster way to do this problem without using charts, I would greatly take it into consideration. Thanks!