In a certain culture of bacteria the rate of increase is proportional to the number present.
(i) if it is found that the number doubles in hours, how many may be expected at the
end of 12 hours. (ii) if there are 10ସ
at the end of hours and 4.10ସ
at the end of 5 hours,
how many were in the beginning.
Answers
Given : culture of bacteria the rate of increase is proportional to the number present. Number doubles in a hour ,
To find : how many may be expected at the end of 12 hours
Solution :
Let N be the number of bacteria present at time t
bacteria grows at a rate proportional to the number of bacteria present.
dN/dt = kN
=> dN/N = k dt
integrating both sides
=> ln (N) = kt²/2 + a
at t = 0 Let Bacteria = b
=> ln (b ) = a
=> b = eᵃ
Bacteria Doubles in 1 hr
ln (2b) = k*1²/2 + ln (b)
=> ln(2) = k/2
=>k = 2ln(2)
ln (N) =2ln(2)t²/2 + ln (b )
=> ln (N) = ln(2)t² + ln (b )
at t = 12
=> ln (N) = ln(2)*12² + ln (b )
Learn more:
A culture of bacteria grows at a rate proportional to the number of ...
https://brainly.in/question/17008734
In a culture, the bacteria count is 1,00,000. The number is increased ...
https://brainly.in/question/3663816