The rate of growth of bacteria in a culture is proportional to the number of bacteria present,  and the bacteria count is 1000 at initial time at t=0. The number of bacteria is increased by 20% in 2 hours. If population of bacteria is 2000 after  kloge65hours, then  kloge22is equal to

Let x be the number of bacteria present at time t, it givesdxdt=kx            Integrate both sides ⇒lnx=kt+c,            The initial condition is0,1000            Hencec=ln1000            At t = 2,x=1000+1000×20100=1200            Log 1200=2k1+log1000⇒2k1=log12001000=log65⇒k1=12log65   ∴logx=12log65t+log1000                                                        Given        log2000=12log65.k+log1000log65    ⇒k=2log2                 kloge22=22=4