The population of humorville is 8500 people. In this town Jokes travel fast, in one hour, each person who hears a joke tells three other people who have not heard it, and tells no one else. Last Friday, a visitor from out of town told the police chief a new joke at 10:00 a.m. how long did it take for everyone in Humorville to hear the joke?

Answer 1

after n hours, 1+3+3^2+3^3 + ... + 3^n = (3^n - 1)/2 people have heard the joke.

So, we want n such that

(3^n - 1)/2 = 8500
3^n = 17001
n = 8.8666 hours = 8 hrs 52 min

Answer 2

sum of 1 + 3 + 9 + 27 ..... 3^(n-1)
geometric series
a = 1
r = 3