The population of a city increases at a rate proportional to the population at that time. If the population of the city increase from 20 lakhs to 40 lakhs in 30 years, then after another 15 years the population is

Step-by-step solution

We have dP dt P dP dt = kP dP dt = k d t P = kt + c From given data, we write aligned & 20= k (0)+ c c = 20 & P = kt + 20 & Also 40=30 k + 20 & 40- 20=30 k k = 1 30 2 & P = ( 2 30 ) t + 20 & When t =30+15=45 & P = ( 2 30 )(45)+ 20=( 2) ( 3 2 )+ 20 & = (2)^ 3 2 + 20= (2 2 20) & P =40 2 lakhs aligned