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

ConceptRate of Change of Bodies Or Quantities

#### 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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