Suppose Y(t) = 25e^3t + 12 represents the number of bacteria present at time t minutes. At what time will the population reach 100 bacteria? ( Note: Answers are expressed in terms of natural logarithm

Given:

The given function is:

Where Y represents the number of bacteria present at time t minutes.  

To find:

The time taken by bacteria population to reach 100 bacteria.

Solution:

We have,

Putting , we get

Divide both sides by 25.

Taking ln on both sides, we get

Divide both sides by 3.

Therefore, the required time is minutes.