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#