# math

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 frieday, 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?

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1. at 10:00 one person heard it
at 11:00 1 + 3 heard it
at 12:00 1 + 3 + 9 hear it
..
.

looks like a geometric series with
a=1
r = 3, and Sn = 8500

1(3^n - 1)/(3-1) = 8500
3^n - 1 = 17000
3^n = 17001
n = log 17001/lg3
n = 8.86 hours or appr 9 hours

so at 19:00 hrs, or in the US way of stating time, at 7:00 pm

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2. ie

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