In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

let y be the number of bacteria at any instant t.

Given that the rate of growth of bacteria is proportional to the number present

Separating variables,

Integrating both sides,

⇒ log y = kt + c -i)

Let y’ be the number of bacteria at t = 0.

⇒ log y’ = c

Substituting the value of c in

⇒ log y = kt + log y’

⇒ log y- log y’ = kt

Also, given that number of bacteria increases by 10% in 2 hours.

Substituting this value in

So, becomes

Now, let the time when number of bacteria increase from 100000 to 200000 be t’.

So from

So bacteria increases from 100000 to 200000 in hours.

22