The rate of increase of population of a country is proportional to the number present. If the population doubles in 50 years, then the time taken by it to become four times of it self is

Step-by-step solution

We have dp dt p dp dt = kp dp p = kdt p = kt + c (1) When t =0, p = p ₀ (initial population) c = p ₀ ( p p ₀ )= kt (2) When t =50, p =2 p ₀ , we get 2=50 k k = 1 50 2 ( p p ₀ )= t 50 2 When p =4 P ₀ 4= t 50 2 2 2= t 50 2 t=100 years This problem can also be solved as follows : Let initial population =p Population doubles in 50 years After 50 years, population =2 p After 100 years, population =4 p