# A sample of 2000 bacteria selected from this population reached the size of 2266 bacteria in five hours. How do you find the continuous growth rate per hour?

Jul 2, 2016

Continuous growth rate per hour is 2.53%

#### Explanation:

Let the growth rate be x% in one hour.

So $2000$ will become $2000 \left(1 + \frac{x}{100}\right)$

and in five hours it will become $2000 {\left(1 + \frac{x}{100}\right)}^{5}$

Hence $2000 {\left(1 + \frac{x}{100}\right)}^{5} = 2266$

or ${\left(1 + \frac{x}{100}\right)}^{5} = \frac{2266}{2000} = 1.133$

Hence $5 \log \left(1 + \frac{x}{100}\right) = 0.05423$

or $\log \left(1 + \frac{x}{100}\right) = \frac{0.05423}{5} = 0.01085$

Hence $1 + \frac{x}{100} = 1.0253$ or

$\frac{x}{100} = 0.0253$ and $x = 2.53$