Question

A petri dish has 10, 000 bacteria in it. After 4 hours the bacteria’s population increased to 20,000. If the number of colonies grows exponentially, write a formula for the number of bacteria in the dish at any time t, where t is in hours

Answer 1

Answer:

$P(t) = 10000e^{0.1733t}$

Step-by-step explanation:

The population of bacteria grows exponentially, which means that it can be represented by a function in the following format:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial population and r is the growth rate.

A petri dish has 10, 000 bacteria in it.

This means that $P(0) = 10000$. So

$P(t) = 10000e^{rt}$

After 4 hours the bacteria’s population increased to 20,000.

This means that $P(4) = 20000$, and we use this to find the growth rate. So

$P(t) = 10000e^{rt}$

$20000 = 10000e^{4r}$

$e^{4r} = \frac{20000}{10000}$

$e^{4r} = 2$

$\ln{e^{4r}} = \ln{2}$

$4r = \ln{2}$

$r = \frac{\ln{2}}{4}$

$r = 0.1733$

So, the formula is given by:

$P(t) = 10000e^{0.1733t}$