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