If the population of the country doubles in 50 years, the number of years it triples under the assumption that the rate of increase is proportional to the number of inhabitants

'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.