(adsbygoogle = window.adsbygoogle || []).push({}); 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)

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# Homework Help: Logistic Integral Equation

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