The population of a town has grown at an annual rate of approximately 2.7%. How long will it take for its population of 18 450 people to double at this growth rate?
So basically, all you have to do is set the doubled population equal to the original times the rate of change to the x-1nth power.
The beginning population is irrelevant...we have
2 = (1 + .027)^t where t is the time to double
Take the log of both sides
log 2 = log ( 1 + .027)^t and we can write
log 2 = t * log (1 + .027) divide both sides by log (1 + .027)
log (2) / log (1 + .027) = t ≈ 26 years