Question

The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 h, then in 25 h its number would be 

(A) 8 times the original 

(B) 16 times the original 

(C) 32 times the original 

(D) 64 times the original

Answer 1

Answer is (C) 32 times the original

Let P₀ be the initial population and let the population after t years be P. Then

dP/dt = kP ⇒ dP/P = kdt

On integrating, we have logP = kt + c

At t = 0, P = P₀ 

Therefore,

logP₀ = 0 + c. So,

When t = 25h, we have