The population of a country increases at a rate proportional to the number of inhabitants.$f$ is the population which double in 30 years, then the population will triple in approximately

Let population $=x,$at time t years, 
Given $\frac{dx}{dt}\propto x$

Or $\frac{dx}{dt}=kx$ ,where k is a constant of proportionality

Or$\frac{dx}{x}=kdt.$ .Integrating, we get $\ln x=kt+\ln c\text{ or }\frac{x}{c}=e^{kt}\text{ or }x=c{e}^{kt}$

If initially, i.e., when time
 $$\begin{gathered} t=0,x=x_0\text{, then }{x}_0=c{e}^0=c \\ \therefore x=x_0{e}^{kt} \end{gathered}$$

Given $x=2x_0$ when $t=30.$Then $2x_0=x_0{e}^{30k}\text{ or }2=e^{30k}\therefore \ln 2=30k\to \left(1\right)$

To find t, when t triples, $x=3x_0\text{. }$ Thus,

$$\begin{gathered} 3x_0=x_0{e}^{kt}\text{ or }3=e^{kt} \\ \therefore \ln 3=kt\to \left(2\right) \end{gathered}$$

Dividing equation (2) by (1), $\frac{t}{30}=\frac{\ln 3}{\ln 2}\text{ Or }t=30\times \frac{\ln 3}{\ln 2}=30\times 1.5849=48\text{ years }(\text{ approx..) }$