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Homework Help: Constructing an equation

  1. Jan 28, 2007 #1
    Here's the question:
    A bacteria culture starts with 820 bacteria and grows at a rate proportional to its size. After 3 hours there will be 2460 bacteria.

    (a) Express the population after t hours as a function of t.

    I tried y=y'+820, so -y'+y=820
    p(t)=1
    mu(t)=e^t

    I carried this out (multiplying both sides by mu(t) and finding the integral of both sides) and it's not right.

    I really don't even know where to start - is finding mu(t) even the right approach?

    Thanks a lot.
     
  2. jcsd
  3. Jan 28, 2007 #2

    cristo

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    Staff Emeritus
    Science Advisor

    Your first equation is incorrect.
    The correct equation for this system would be: [tex]\frac{dy}{dt}=ky[/tex], where k is the constant of proportionality; your equation omitted this!

    Try integrating this. The numbers are there as the boundary conditions of the system, to enable you to calculate the constants.
     
  4. Jan 28, 2007 #3
    Yep, that was it. Thanks.
     
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