The population of humorville is 8,500 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 10:00a.m. How long did it take for everyone in Humorville to hear it?

Answer 1

after one hour, 3
after two hours, 9+3
after three hours, 27+9+3

so this is a geometric series,

3,9,27, ...3^t

The sum of a geometric series is

St=(1-3^t)/(1-3)=(1-3^t)/-2

or
8500*(-2)=1-3^t
-17000=-3^t
log17000=tlog3
t=8.86, but t is an integer, so t=9 hours.

check my work.