The population of a village increases at a rate proportional to the population at that time. In a period of 10 years the population grew from 20,000 to 40,000 , then the population after another 20 years is

Step-by-step solution

We have dP dt P dP dt = kP dP P = kdt P = kt + c We have: when t=0, P=20000 and when t=10, P=40000 20000= c Now 40000=10 k + 20000 ( 40000 20000 )=10 k k = 1 10 2 P= ( 1 10 2 ) t+ 20000 When t=30 , we write P= 30 10 2+ 20000= [(8)(20000)] P=160000 This problem can also be solved as follows : From given data, we say that population doubles in 10 years. In next 10 years, population changes from 40,000 to 80,000 . In 10 years after that, population changes from 80000 to 160000