Question
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?
Solution
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.
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 = 0Now,
...(3)Let the bacteria be 2,00,000 from 1,00,000 in
hoursi.e.
