Q. 4

In a culture, the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 20000, if the rate of growth of bacteria is proportional to the number present?

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 = 100000 when t = 0 sec


Putting the value in equation (1)


log|C| = kt + a


log|100000| = 0 + a


a = log|100000| ……(2)


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


log|C| = kt + log|100000|


log|C| – log|100000| = k t []


log ( = kt ……(3)


Also, at t = 2 years, = 110000


From equation(3),we have


kt = log (


k×2 = log (


k = ……(4)


Now, equation (3) becomes,



Now, let t1 be the time for the population to reach 200000





The time require for the population to be 200000 = hours


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