The rate of growth of bacteria is proportional to number present. If initially there were 1000 bacteria and the number doubles in 1 hour then the number of bacteria after 2 1 2 hours are (Given 2 =1.414 )

Step-by-step solution

The rate of growth is proportional to the number present d N dt N d N dt = kN d N N = k dt On integrating we get dN N = k dt N = kt + C When t =0, ~N =1000 C = 1000 N = kt + 1000 ( N 1000 )= kt N =1000 e ^ kt ...(1) When t =1, ~N =2000 e ^ k =2 N =1000 2¹ [ from (1) ] When t=2 1 2 , we get N =1000 2^ 5 2 =1000 4 2 =1000 4 1.414=5656