Q. 35.0( 3 Votes )

The rate of growth of a population is proportional to the number present. If the population of a city doubled in the past 25 years, and the present population is 100000, when will the city have a population of 500000?

[Given loge 5 = 1.609, loge 2 = 0.6931]

Answer :

Let the initial population be Po .

And the population after time t be P.


According to question,






Integrating both sides, we have


= k∫dt


log|P| = kt + c ……(1)


Given, we have P = Po when t = 0 sec


Putting the value in equation (1)


log|P| = kt + c


log|Po| = 0 + c


c = log|Po| ……(2)


Putting the value of c in equation (1) we have,


log|P| = kt + log|Po|


log|P| – log|Po| = k t


(log |P| – log|Po|) = kt []


log ( = kt ……(3)


Now, the population doubled in 25 years.


Let P = 2Po at t = 25 years


kt = log (


k×25 = log (


k = ……(4)


Now, equation (3) becomes,



Now, let t1 be the time for the population to increase from 100000 to 500000





(log5 = 1.609 and log2 = 0.6931)


t1 = 58


The time require for the population to be 500000 = 58 years.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz on DIfferential CalculusFREE Class
Functional Equations - JEE with ease48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses