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

Step-by-step solution

Let initial population =P₀ and let P be the population at time t We have dP dt = 5 P 100 d P d t = P 20 d P P = 1 20 d t P= 1 20 t+C ....(1) When t=0, P=P₀ P ₀=0+ C C = P ₀ From (1), ( P P₀ )= t 20 ....(2) When P=2 P₀ , we get 2= t 20 t=20( 2)=20 0.6912=13.8240 years