Question

In a lab experiment, 590 bacteria are placed in a petri dish. The conditions are such

Answer 1

Answer:

There would be 859 bacteria after 13 hours.

Step-by-step explanation:

The population of bacteria after t hours is given by the following equation:

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

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

The number of bacteria is able to double every 24 hours.

This means that $P(24) = 2P(0)$. So

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

$2P(0) = P(0)e^{24r}$

$e^{24r} = 2$

$\ln{e^{24r}} = \ln{2}$

$24r = \ln{2}$

$r = \frac{\ln{2}}{24}$

$r = 0.0289$

590 bacteria are placed in a petri dish.

This means that P(0) = 590. So

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

$P(t) = 590e^{0.0289t}$

How many bacteria would there be after 13 hours, to the nearest whole number?

This is P(13).

$P(t) = 590e^{0.0289t}$

$P(13) = 590e^{0.0289*13} = 859$

There would be 859 bacteria after 13 hours.