The population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 80 thousand in 40 years, then the population in another 40 years will be

Step-by-step solution

Let p be the population at time t years. Then dp dt = kp dp p = kdt Integrating on both sides, we get p = kt + c when t =0, p =40000 aligned & 40000=0+c & & c = 40000 aligned aligned & p = kt + 40000 & ( p 40000 )= kt aligned When t =40 years, p =80000 aligned & ( 80000 40000 )=40 k & k = 1 40 2 aligned ( p 40000 )= 1 40 2 t Population after another 40 years, i.e., t =80 years, we have aligned & ( p 40000 )= 1 40 2 80 & p 40000 =2 2 & p 40000 =4 & p =16,0000 aligned