What hour did the town hear the joke?!

Question

The population of Mound is 8754 word travels fast in this town. In one hour, every person who hears a joke tells 3 other people who have not heard the joke. At 10am, a visitor told Mr. David a joke. By what hour did everyone in the town hear the joke?!

Answer 1

This is a problem in exponential growth.  The tripling period is 1 hour.  For time t in hours elapsed from the first telling of the joke, the number of people who heard it is given by

 

n(t) = n₀ (3)^t/1

 

n₀ = 1

 

n(t) = 3^t

 

Set n(t) = 8754 and solve for t.

 

8754 = 3^t

 

log8754 = t log3

 

t = log8754 / log3 ≅ 8.262 hours

 

Add t hours to 10 am.