HSC Arts 12th Board ExamMaharashtra State Board
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The rate of growth of bacteria is proportional to the number present. If, initially, there were 1000 bacteria and the number doubles in one hour, find the number of bacteria after 2½ hours. - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

The rate of growth of bacteria is proportional to the number present. If, initially, there were
1000 bacteria and the number doubles in one hour, find the number of bacteria after 2½
hours. 

[Take `sqrt2` = 1.414]

Solution

Let ‘N’ be the number of bacteria at time’t ’

`therefore "dN"/dt  ooN`

`"dN"/dt=kN`

`"dN"/N=kdt`

Integrating on both sides, we get

`int"dN"/N=kintdt`

`logN=kt+c`

`when t=0,N=1000`

`c=log1000`

`logN=kt+log1000`

`log(N/1000)=kt`

`N=1000e^(kt)`               ..........(1)

when t = 1 hour, N = 2000

`e^k=2`

`N=1000xx(2)^t`      ....................from (1)

when `t=2 1/2` hours, we get

`N=1000xx(2)^(5/2)`

`=1000xx4xxsqrt2=4000xx1.414`

`N=5656`

Number of bacteria present after `2 1/2` hours is 5656

  Is there an error in this question or solution?

APPEARS IN

 2016-2017 (July) (with solutions)
Question 5.2.2 | 4.00 marks

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Solution The rate of growth of bacteria is proportional to the number present. If, initially, there were 1000 bacteria and the number doubles in one hour, find the number of bacteria after 2½ hours. Concept: Rate of Change of Bodies Or Quantities.
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