In 2015, the population of a small town in Florida is 95. If the population increases 15% every year, approximately what will the population be in 2023?

1 Answer
Apr 25, 2018

95 times 1.15^{8} approx 291

Explanation:

There is a 15% increase every year. This means of course that every year we multiply the current population by 1.15.

The population starts at 95. (2015)
After the first year (2016) it will be 95 times 1.15
After the second year (2017) it will be (95 times 1.15) times 1.15
After the third year (2018) it will be ((95 times 1.15) times 1.15) times 1.15
etc...

This is a rather simple recurrence relation meaning that we can write it as 95 times 1.15^{year}

2023 -2015=8 is the number of years

95 times 1.15^{8} will give us our answer.

95 times 1.15^{8} approx 290.6071719412 people.

Now obviously we cannot have fractions of people so it would make sense to round it to an integer.

291