Question

In a certain culture of bacteria, the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, find the number of times the bacteria are increased in 12 hours.

Answer 1

Let x be the number of bacteria in the culture at time t.

Then the rate of increase is dx/dt which is proportional to x.

On integrating, we get

Since the number doubles in 4 hours, i.e. when t = 4, x = 2x₀

∴ the number of bacteria will be 8 times the original number in 12 hours.