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Modeling survival with a differential equation

  1. Jul 19, 2016 #1
    1. The problem statement, all variables and given/known data
    A health club is opened, the fraction of members still enrolled t months from their initial visit is given by the function f(t)= e-t/20. the club initially accepts 300 members and will accept new members at a rate of 10 per month. How many people will be enrolled 15 months from now.

    2. Relevant equations

    3. The attempt at a solution
    I remember my professor referencing this problem could be done as a differential equation problem instead of a survival/renewal problem (which I can do).

    Following the idea of inflow-outflow, I came up with

    dP/dt= 10 (inflow) - ?

    with P being members

    I'm not sure how to take the fraction of people and make that into a rate.
    Once I figure that out I could likely solve the differential normally for P.
  2. jcsd
  3. Jul 20, 2016 #2
    Okay, here's a hint. If f(t) represents the fraction of people still enrolled after their initial visit, what does 1 - f(t) represent?
  4. Jul 20, 2016 #3

    Ray Vickson

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    Are you saying you do not know what 50% of 300 works out to? That is what you would have if ##f(t) = 0.5## applied to the initial 300.
    Last edited: Jul 21, 2016
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