How to satisfy a logistic growth equation?

Discussion in 'Jevic Transportation' started by Joyce Sullivan, Jul 30, 2008.

  1. Joyce Sullivan

    Joyce Sullivan New Member

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    Two bacterial populations, Q(t) and Z(t) are assumed to grow according to Euler exponential growth model, with parameters a and b. Suppose that the two populations are grown together in a beaker. W(t) = Q(t) / (Q(t) + Z(t)) to be the fraction of the total population of Q type. Using differential equations for Q and Z, show that W(t) satisfies a logistic growth equation.
     
  2. longhaul

    longhaul Member

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    does that mean u swallow or spit...........:hysterical:
     
  3. DoorMatt

    DoorMatt Member

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    Let
    Q(t) = Q(0)exp(at)
    Z(t) = Z(0)exp(bt)

    then
    W(t)
    = Q(0)exp(at)/(Q(0)exp(at) + Z(0)exp(bt))
    = 1/[1 + c*exp((b-a)t)]
    where c = Z(0)/Q(0)
    This gives
    W(t)*(1 + c*exp((b-a)t)) = 1
    and
    W(t) = 1 - W(t)*c*exp((b-a)t)
    and
    c*exp((b-a)t) = (1 - W(t))/W(t)

    Taking derivatives, we get
    W'(t) = -W'(t)*cexp((b-a)t) - W(t)*c*(b-a)*exp((b-a)t)
    or
    W'(t)(1 + c*exp((b-a)t)) = -W(t)*(b-a)*c*exp((b-a)t)
    or
    W'(t)/W(t) = -W(t)*(b-a)*(1 - W(t))/W(t)
    or
    W'(t) = -(b-a)*W(t)*(1-W(t))

    This is the logistic differential equation

    No, you stick your head between your legs and kiss your *** goodbye!
     
  4. wizzard-100

    wizzard-100 Member

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    Al

    No that's the difference between like and love.

    Joyce, you joined this board today and this is your first post. Jesus what a waste of time posting meaningless drivel.
     
  5. jevic9090

    jevic9090 Member

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    Wat to Go

    Way to Go Door Matt. Guess you stayed awake in calculus class:biglaugh:
     
  6. xeastend

    xeastend Active Member

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    Good gozintas.
    Now can you blind side into an alley dock??
     
  7. DoorMatt

    DoorMatt Member

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    Not only can I blind it into an alley dock, I can do with a road tractor and a 53' trailer slid all the way back during rush hour across three lanes of city traffic while smoking a cigar and singing along with Jimmy Buffett and not rub my tires.
     
  8. notneb

    notneb Member

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    now i would like to see that one.
     
  9. jevic9090

    jevic9090 Member

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    i got $5.00 that says he marks the bill " straight truck only". and blows it off
     
  10. lipripper

    lipripper New Member

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    WTF is she HOT ? if she's Hot I think she's right
     

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