'x' be the population at a time 't' in years ,
$\frac{\mathrm{dx}}{\mathrm{dt}}\propto \mathrm{x}\Rightarrow \frac{\mathrm{dx}}{dt}=\mathrm{kx}$, integration gives
$x=x_0{\mathrm{e}}^{kt}$ is the population at time t = 0.
Since it double in fifty years at t = 50.
We must have x = 2x₀
Hence, $2{\mathrm{x}}_0={\mathrm{x}}_0{\mathrm{e}}^{50\mathrm{k}}\Rightarrow \mathrm{k}=\frac{1}{50}\log 2$ , to find t,
it triple x = 3x₀ gives $\mathrm{t}=\frac{50\log 3}{\log 2}=80\text{ years }$approximately.