Q. 275.0( 1 Vote )

The rate of increase of bacteria in a culture is proportional to the number of bacteria present, and it is found that the number doubles in 6 hours. Prove that the bacteria becomes eight times at the end of 18 hours.

Answer :

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

According to the 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| C0|

log|C| – log| C0| = k t []

log ( = kt ……(3)

Also, at t = 6 years, C = 2C0

From equation(3),we have

kt = log (

k×6 = log (

k = ……(4)

Now, equation (3) becomes,

Now, C = 8C0

t = 18

The time required = 18 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