In a culture the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present?

Question

Philoid · Accepted Answer

Let y be the bacteria count, then, we have,

rate of growth of bacteria is proportional to the number present

So,

Where c is a constant,

Then, solving the equation we have,

Where k is constant of integration

And we have for t = 0, y = 10000,

…(i)

For t = 2hrs, y is increased by 10% i. e. y = 110000

⇒ from (i)

⇒

When y = 200000, we have,

⇒

Hence, t =