Question

A community has a population of 25000 which increases by 15% every year. What will be the population of the community after 6 years?

Answer 1

`57826` people

Explanation:

An increase of 15% as a decimal is given by `1.15`.

`x*1.15 = x(1 + 0.15) = x + 0.15x`

So, we have to multiply by 1.15, then multiply the result by 1.15 and so on until we get to 6 years. For example, for 3 years it would be

`((25000*1.15)*1.15)*1.15`

Luckily, we can group the 1.15s together, like so:

`25000*(1.15)^n`

Where `n` is the number of years we are looking at. In this case, `n=6` so final population is given by:

`25000*1.15^6 = 57826.5 = 57826` people