Question

The population of Mussman, Maine is 13,500 and grows at an annual rate of 6.5%. How long will it take the population of Mussman, Maine to reach 27,000 residents?

Answer 1

about 1.6090405507426917 years (round this)

Explanation:

This question requires reverse thinking. This type of problem is usually presented like 13,500 people are there to start with and it increases by 6.5 yearly, how much will it be in a year? But this time we have to find the years and we have the end population value.

First write equation:

13,500(0.065)^x = 27000

Simplify by dividing:

0.65^x = 0.5

*Use property of log (for isolating x):

x(log(0.65)) = log(0.5)

Isolate x:

x = log(0.5)/log(0.65)

x = 1.6090405507426917

*the reason why we did log was because we need the x to not be in an exponent for but to be normal. So log makes us able to write it like that. Same works with ln or natural log. For continuously compounding or continuously depreciating you would use ln.