The population of a country doubles in 40 years. Assuming that the rate of increase is proportional to the number of inhabitants, the number of years in which it would treble itself is

[c] Let the initial population be x0 and it is x in t years, then the differential equation is$dxdt=kx,kisacons\tan t$⇒dxx=kdt.Integrating we get$\log x+kt+C?\left(i\right)$When t=0,x=x0⇒c=logx0$Then\mathfrak{o}m\left(i\right)\log x=kt+\log x0$⇒logxx0=kt                                             ? (ii)$Nowwhen$⇒logxx0=2⇒log2=k.40⇒k=log240$\therefore \left(ii\right)becomes\log \times 0=\log 240.t$Next put xx0=3⇒t=40log3log2