Hello, calc_help123!

The rate of change in the number of bacteria in a culture is proportional to the number present.

In a certain laboratory experiment, a culture had 10,000 bacteria initially,

20,000 a time minutes and 100,000 bacteria at minutes.

A) In terms of only, find the number of bacteria in the culture a any time

Let = population of bacteria.

We have: .

. . . .

When

The function (so far) is: .

Divide [2] by [1]: .

. .

The function is: .

. . Hence: .

B) How many bacteria were there after 20 minutes?

When

C) How many minutes had elasped when the 20,000 bacteria were observed?

We have: .

Take logs: .

Therefore: .