# A sample of 2600 bacteria selected from this population reached the size of 2817 bacteria in two hours. How do you find the continuous growth rate per hour?

Oct 17, 2015

Each hour, the population increases by a factor of $\sqrt{\frac{2817}{2600}} \approx 1.0409$, that is an increase of 4.09%

#### Explanation:

If $r$ is the factor by which the population grows each hour, then starting with a population ${P}_{0}$, the population after $t$ hours will be:

$P \left(t\right) = {P}_{0} {r}^{t}$

In our case ${P}_{0} = 2600$, $t = 2$ and $P \left(2\right) = 2817$.

So

$2817 = 2600 {r}^{2}$

Hence ${r}^{2} = \frac{2817}{2600}$

So $r = \sqrt{\frac{2817}{2600}} \approx 1.0409$

To express this as a percentage, subtract $1$ and multiply by $100$ to get 4.09%