Q. 65.0( 1 Vote )

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs, find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present.

[Given loge 3 = 1.0986, e2.1972 = 9]

Answer :

Let the count of bacteria be C at any time t.

According to question,



where k is a constant




Integrating both sides, we have


= k∫dt


log|C| = kt + a……(1)


Given, we have C = C0 when t = 0 sec


Putting the value in equation (1)


log|C| = kt + a


log| C0| = 0 + a


a = log| C0| ……(2)


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


log|C| = kt + log|100000|


log|C| – log| C0| = k t []


log ( = kt ……(3)


Also, at t = 5 years, C = 3C0


From equation(3),we have


kt = log (


k×5 = log (


k = ……(4)


Now, equation (3) becomes,



Now, let C1 be the number of bacteria present in 10 hours, as






Let the time be t1 for bacteria to be 10 times






The time required for = hours


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