Math
posted by Erica on .
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?

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=(13^t)/(13)=(13^t)/2
or
8500*(2)=13^t
17000=3^t
log17000=tlog3
t=8.86, but t is an integer, so t=9 hours.
check my work.