# There are 225 wolves in a state park. The population is increasing at the rate of 15% per year. When will the population reach 500?

Apr 16, 2016

Between years 5 and 6.

#### Explanation:

Population after $n$ years is given by the formula
$\textcolor{w h i t e}{\text{XXX}} {P}_{n} = 225 \times {\left(1.15\right)}^{n}$

$\textcolor{w h i t e}{\text{XXX}} P n = 500$
$\textcolor{w h i t e}{\text{XXX}} 225 \times {\left(1.15\right)}^{n} = 500$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow {1.15}^{n} = \frac{500}{225} = \frac{20}{9}$
$\textcolor{w h i t e}{\text{XXX}} {\log}_{1.15} \left(\frac{20}{9}\right) = n$
$\textcolor{w h i t e}{\text{XXX}} {\log}_{1.15} \left(\frac{20}{9}\right) \approx 5.7133$