Question

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?

Answer 1

`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`