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Logistic Integral Equation

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data

    This a problem that I didn't get completely right after a test, so I wouldn't mind figuring out what were my errors.

    A state game commission releases 40 elk into a game refuge. After 5 years, the elk population is 104. The commission believes that the environment can support no more than 4000 elk.

    a) find the specific solution to this differential equation; be sure to find values for all constants.

    2. Relevant equations

    dP/dt = kP(1- P/4000) 40≤ P ≤ 4000 A = (K - P initial)/K P = K/(1 + Ae^-kt)

    3. The attempt at a solution

    A = (K - P initial)/K
    A = (4000 - 40)/4000
    A = .99

    P = K/(1 + Ae^-kt)
    104 = 4000/(1 + .99e^-k5)
    104(1 + .99e^-k5) = 4000
    104 + 102.96e^-k5 = 4000
    102.96e^-k5 = 3896
    e^-k5 = 37.84
    -5k = ln (37.84)
    k = -1/5 ln (34.84)
     
  2. jcsd
  3. Oct 19, 2011 #2

    Mark44

    Staff: Mentor

    What's your question?
     
  4. Oct 19, 2011 #3
    I needed to find k in the equation.
     
  5. Oct 19, 2011 #4

    Mark44

    Staff: Mentor

    You found one. Does it work in your differential equation?

    IOW, does your solution give P(0) = 40 and P(5) = 104?
     
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