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 denote the bacteria at any time t.
 From the given condition,
                             where k is the constant of proportionality.
Separting the variables and integrating, we get,
                     
                                ...(1)
Let  be bacteria at time t = 0

Now,                          

                         ...(3)
Let the bacteria be 2,00,000 from 1,00,000 in  hours
i.e.