## Book: Mathematics Part-II

### Chapter: 9. Differential Equations

#### Subject: Maths - Class 12th

##### Q. No. 22 of Exercise 9.4

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##### In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

let y be the number of bacteria at any instant t.

Given that the rate of growth of bacteria is proportional to the number present  Separating variables, Integrating both sides, log y = kt + c -i)

Let y’ be the number of bacteria at t = 0.

log y = c

Substituting the value of c in log y = kt + log y

log y- log y = kt Also, given that number of bacteria increases by 10% in 2 hours.  Substituting this value in   So, becomes  Now, let the time when number of bacteria increase from 100000 to 200000 be t’. So from  So bacteria increases from 100000 to 200000 in hours.

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