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a bacteria culture starts with 420 bacteria and grows at a rate proportional to its size. after 6 hours there will be 2520 bacteria.

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maryamkincsem

Population growth rate of the bacterial culture can be expressed as a function of time as N = [tex]e^{kt + C}[/tex]

Step-by-step explanation:

If we assume the number of bacteria at any time (t) is (N). Then, the population of bacterial culture at that time is given by

N = N (t)

It is also given that the rate at which the bacterial culture will grow is proportional to its size. So, the growth rate is given by

dN/dt ∝ N

Removing the sign of proportionality, we get a constant

dN/dt = KN

We get

∫1/N dt = ∫K dt

After integration

ln N = Kt + C

N = [tex]e^{kt + C}[/tex]

You can learn more about population growth rate from
https://brainly.com/question/1437549
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The question is incomplete. Therefore, the complete question is

A bacteria culture starts with 520 bacteria and grows at a rate proportional to its size. After 6 hours there will be 3120 bacteria. ?

1) Express the population after t hours as a function of t. population:

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