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

Aug 4, 2016

$57826$ people

#### Explanation:

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

$x \cdot 1.15 = x \left(1 + 0.15\right) = x + 0.15 x$

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

$\left(\left(25000 \cdot 1.15\right) \cdot 1.15\right) \cdot 1.15$

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

$25000 \cdot {\left(1.15\right)}^{n}$

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

$25000 \cdot {1.15}^{6} = 57826.5 = 57826$ people