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Bacteria Growth Problem.

  1. May 11, 2005 #1
    My friend had to do this problem in Calculus BC. I'm no good at calculus, but I decided it was be fun for someone to figure it out for me.

    A bacteria culture starts with 500 bacteria and grows at a rate proportional to its size. After 3 hours there are 8000 bacteria.
    (a) Find an expression for the number of bacteria after t hours.
    (b) Find the number of bacteria after 4 hours.
    (c) Find the rate of growth after 4 hours.
    (d) When will the population reach 30,000?

    I think it involves differential equations.
     
  2. jcsd
  3. May 11, 2005 #2
    :rofl: :rofl: :rofl:

    Start with [tex]y=Ae^{kt}[/tex]
     
  4. May 11, 2005 #3
    Yeah that amused me too :smile: .I'd probably start a little earlier:

    Growth proportional to size implies.....

    [tex]\frac{dy}{dt}=ky[/tex]

    with the intial condition [tex]y(0)=500[/tex] and the time t = 3 (in hours!) condition [tex]y(3)=8000[/tex].

    Your mission, should you choose to accept it, is to find the general solution to the DE above, and the values of k and the constant of integration A.

    That's the model, the rest should be ok?
     
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