Answer to Question #349161 in Differential Equations for cookies

Question

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?

Answer 1

Population grows according to the function

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

Given

$$P(0)=1000000$$

$$P(2)=5000000$$

Substitute

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

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

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

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

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

$$P(5)=11180340$$

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