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

Step-by-step solution

Let x be the number of bacteria in certain culture at time t . Then rate of increase is d x d t which is proportional to x . array l dx dt x dx dt = Kx dx x = Kdt dx x = K dt x = Kt + c ...(1) Initially when t =0, let x = x ₀ x =0+ c c = x ₀ from (1) x = kt + x ₀ ( x x ₀ )= Kt ...(2) array Given number doubles in 4 hrs i.e. when t=4, x=2 x₀ ( 2 x ₀ x ₀ )=4 ~K K = 1 4 2 from (2) ( x x₀ )= t 4 2 When t =12 ( x x₀ )= 12 4 2=3 2= 2³= 8 x x₀ =8 x=8 x₀ This problem can be alternatively solved as follows : Let the intial