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Learning Curve

  1. Jun 25, 2008 #1
    I'm not even sure how to start this question

    K'(T)=k(M-K(t))
    M=total knowledge

    suppose that:
    M=100
    K(0)=0
    and
    K(2)=50

    does this mean
    k'(0)=k(100-0)
    and
    k'(2)=K(100-50)
     
  2. jcsd
  3. Jun 25, 2008 #2

    Defennder

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    Homework Helper

    This looks like one of those ODE modeling questions. I think you have to elaborate more on what K, k, T and t are. More specifically tell us which variables the aforementioned functions are of. And K'(T) is dK/dt or dK/dT ?
     
  4. Jun 25, 2008 #3
    K(t)is the total knowledge about how to perform at task at time t

    K'(t) or the rate of change in K(t) is proportional to what we do not know yet or
    K'(t)=k(M-K(t)) where M is total knowledge

    it takes two years to learn 50% of the task, how long does it take to learn 75%
     
  5. Jun 25, 2008 #4

    Defennder

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    Ok I take it that M is a constant and not a function of t and T and t are the same thing. k is also an unknown constant. So you have:

    [tex]\frac{dK}{dt} = k(M-K)[/tex]

    So this is a 1st order ODE. It's clearly separable. Solve it for K(t) and plug in the given values of K(0) and K(2) to solve for the constant of integration and k.
     
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