Question

Help!!!

Answer 1

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;

$P = 100e^{0.60t}$   ......[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];

$400 = 100 e^{0.06t}$

Divide both sides by 100 we get;

$4 = e^{0.06t}$

Taking ln both sides we get;

$ln 4 = ln e^{0.06t}$

Since; $ln e^x = x$

then;

$ln 4 = 0.06 t$

Divide both sides by 0.06 we get;

$t = \frac{ln 4}{0.06}$

or

$t =\frac{1.38629436112}{0.06} =23.104906$ hours

Therefore, the time it will take is, t = 23.1 (round to the nearest tenth)