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]
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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:
