Answer:
Time it will take t = 23.1 (round to the nearest tenth)
Step-by-step explanation:
Given: A population of bacteria is growing exponentially;
According to the model;
[tex]P = 100e^{0.60t}[/tex] ......[1]; where P is the number of colonies and t be the time measured in hours.
After how many hours will 400 colonies be present.
Substitute value of P = 400 in [1];
[tex]400 = 100 e^{0.06t}[/tex]
Divide both sides by 100 we get;
[tex]4 = e^{0.06t}[/tex]
Taking ln both sides we get;
[tex]ln 4 = ln e^{0.06t}[/tex]
Since; [tex]ln e^x = x[/tex]
then;
[tex]ln 4 = 0.06 t[/tex]
Divide both sides by 0.06 we get;
[tex]t = \frac{ln 4}{0.06}[/tex]
or
[tex]t =\frac{1.38629436112}{0.06} =23.104906[/tex] hours
Therefore, the time it will take is, t = 23.1 (round to the nearest tenth)
