# A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 13,000. What was the initial size of the bird population?

Dec 30, 2016

$2298$

#### Explanation:

The population is modelled by the formula:

$P \left(t\right) = {p}_{0} \cdot {2}^{\frac{t}{10}}$

where ${p}_{0}$ is the initial population and $t$ the time in years.

So we have:

$13000 = P \left(25\right) = {p}_{0} \cdot {2}^{\frac{25}{10}} = {p}_{0} \cdot {2}^{\frac{5}{2}} = 4 \sqrt{2} {p}_{0}$

So the initial population is:

${p}_{0} = \frac{13000}{4 \sqrt{2}} = \frac{13000}{8} \sqrt{2} = 1625 \sqrt{2} \approx 2298$