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Logistic Equation

  1. Mar 27, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm having some difficulty understanding the last step of the following solved problem from my textbook:

    We will compute the equilibrium points of [itex]kP \left( 1- \frac{P}{N} \right) - C[/itex].

    [itex]kP \left( 1- \frac{P}{N} \right) - C =0[/itex]

    [itex]-kP^2+kNP - CN =0[/itex]

    The quadratic equations has solutions

    [itex]P= \frac{N}{2} \pm \sqrt{\frac{N^2}{4}-\frac{CN}{k}}[/itex]


    3. The attempt at a solution

    So if we start off by

    [itex]-kP^2+kNP - CN =0[/itex]

    and using the quadratic equation:

    [itex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/itex]

    I get:

    [itex]P= \frac{-kN \pm \sqrt{(kN)^2-4kC}}{2k}[/itex]

    [itex]= \frac{N}{2} \pm \frac{\sqrt{k^2N^2-4kC}}{2k}[/itex]

    So, why is my answer different from the one in the textbook? And how can I end up with the solution in the book (that I've posted above)? :confused:
     
  2. jcsd
  3. Mar 27, 2012 #2
    [itex]2k = \sqrt{\text{(what?)}}[/itex]
     
  4. Mar 28, 2012 #3
    Oh, I see. I never thought of it. Thank you very much. :smile:
     
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