Question #349161

Initially, there are 1 million bacteria present in a Petri dish. After 2 minutes, there are already 5 million of them. If the bacterial population follows a law of natural growth, how many bacteria should be present in the Petri dish after 5 minutes?


1
Expert's answer
2022-06-09T08:08:34-0400

Population grows according to the function


P(t)=P(0)ektP(t)=P(0)e^{kt}

Given


P(0)=1000000P(0)=1000000

P(2)=5000000P(2)=5000000

Substitute


5000000=1000000ek(2)5000000=1000000e^{k(2)}

ek=5e^k=\sqrt{5}

P(t)=1000000(5)tP(t)=1000000(\sqrt{5})^t

P(5)=1000000(5)5P(5)=1000000(\sqrt{5})^5

P(5)=1000000(55)P(5)=1000000(5\sqrt{5})

P(5)=11180340P(5)=11180340

11180340 bacteria should be present in the Petri dish after 5 minutes.



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