If the population grows at the rate of 5 % per year, then the time taken for the population to become double is (Given 2=0.6912 )

Step-by-step solution

Let P be the population at time t and P ₀ be the initial population. aligned Given dP dt &= 5 P 100 dP P = 1 20 dt P &= 1 20 t + c ...(1) aligned We have t=0, P=P₀ P ₀= c P = t 20 + P ₀ ( P P ₀ )= t 20 ...(2) When P=2 P₀ , we write ( 2 P₀ P₀ )= t 20 2= t 20 t=20(0.6912)=13.824 years