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Slope fields

  1. Apr 12, 2013 #1
    What is the limiting value of P as t->infinity

    dp/dt=0.4P(10-P)

    My attempt at the solution was to serperate the function and get each side in terms of one variable

    dp/(P(10-P)) = 0.4/dt

    [-ln(|p-10|/|p|)]/10=0.4t

    -ln(|p-10|/|p|)=4t
    take e^ of both sides of equation

    (p-10/p)=e^4t and we know that the equation is undefined on the left when the p=10 therefore there is some type of discontinuity. is this correct?
     
  2. jcsd
  3. Apr 12, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    I think this should be 0.4 dt.
    The following line is missing an integration constant.

    That equation is problematic if you want to take the limit of t->infinity. There are better ways to do this, but you can guess the value of p here as well. Oh, and there are brackets missing.
     
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