# A species of bacteria has a population of 250 at 6 a.m. It doubles every 8 hours. Determine the function that models the growth of the population. Determine the population at 9 p.m.?

##### 1 Answer
May 28, 2018

6 a.m. to 2 p.m. population reaches 500.

#### Explanation:

Your equation is

(it is exponential function)

$P = {P}_{0} \times {e}^{k t}$

${P}_{=}$ is the initial population

t is time which is 15 hours.

First, You can compute k (growth rate)

$500 = 250 \times {e}^{k \times 8}$

$2 = {e}^{k \times 8}$

$\ln 2 = k \times 8$

$k = 0.0866$ ${\left(h o u r\right)}^{-} 1$

Now you can calculate the final population

$P = 250 \times {e}^{0.0866 \times 15}$

$P = 917$

which is greater than 500.