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Solving a Verhulst-Pearl model and finding point of inflection

  1. Aug 4, 2009 #1
    1. The problem statement, all variables and given/known data
    find p(T), then find the inflection point on the graph.

    2. Relevant equations
    dp/dt=K*P(1-P/M)
    K is the growth factor
    P=population
    t=time
    (1-p/m)=correction factor
    M=maximum


    3. The attempt at a solution
    I integrated the given equation and got
    ln (p(m-p)+c=kt c=unknown constant
    p(m-p)=e^(kt+c)
    p(m-p)=Ae^kt A=e^c as c=unknown constant therefore A also equals unknown constant

    i said that when t=0, p=Po
    and so i got Po(m-Po)=A

    i fiddled around for a while and got:
    p=m-(Po*(m-Po)*e^(kt))/p
    but as u can see there is still a p on both sides :(
    i thought about making it equal 0 and using the quadratic equation but it will take a lot of work and i dont know if it will work.


    my question is what should i do? have i made a mistake somewhere?
    and also, to find the point of inflection would you just double derive the p(t)?
    or is there another way to do it, ie useing the dp/dt function given.

    any help will be very VERY appreciated.
     
  2. jcsd
  3. Aug 10, 2009 #2
    dw i got it
     
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