The bacteria increases at the rate proportional to the number of bacteria present. If the original number 'N' doubles in 4 hours, then the number of bacteria in 12 hours will be

Step-by-step solution

108. (C) Let x be the number of bacteria at time t . dx dt x dx dt = kx dx x = k dt x = kt + c Initially, i.e. when t=0 , let x=x₀ array l x₀=k 0+c x=k t+ x₀ array c= x₀ x- x₀=k t ( x x₀ )=k t ...(1) Since the number doubles in 4 hrs , i.e. aligned t &=4 and x=2 x₀ ( 2 x₀ x₀ ) &=4 k k = 1 4 2 aligned array l When t=12, ( x x₀ )= 12 4 2=3 2 ( x x₀ )= 8 x=8 x₀ array This problem can be alternatively solved as follows : Original number = N . After four hours, number =2 ~N After eight hours, number =4 ~N After twelve h