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Math Help - Help with seperation of variables word problem

  1. #1
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    Help with seperation of variables word problem

    Here is the problem:

    As you know, when a course ends, students start to forget the material they have learned. One model (called the Ebbinghaus model) assumes that the rate at which a student forgets material is proportional to the difference between the material currently remembered and some positive constant, . A. Let be the fraction of the original material remembered weeks after the course has ended. Set up a differential equation for , using as any constant of proportionality you may need (let ). Your equation will contain two constants; the constant (also positive) is less than for all .

    I've found the equation is k(a-y)
    but it also asks what the initial condition of the equation is?
    and I cannot figure this part out.
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  2. #2
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    Quote Originally Posted by cmerickson21 View Post

    A. Let be the fraction of the original material remembered weeks after the course has ended.

    let the material currently remembered at t = 0 be 1 ... f(0) = 1. y will then be a fraction (percentage) of that material remembered as stated above in bold.
    ...
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  3. #3
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    Thank You. Now I have figured out that the DE is y= a+(1-a)e^(-kt) but I cannot figure out the next part
    C. What are the practical meaning (in terms of the amount remembered) of the constants in the solution ? If after one week the student remembers 90 percent of the material learned in the semester, and after two weeks remembers 86 percent, how much will she or he remember after summer vacation (about 14 weeks)?
    percent =
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  4. #4
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    Thank You. Now I have figured out that the DE is y= a+(1-a)e^(-kt) but I cannot figure out the next part
    C. What are the practical meaning (in terms of the amount remembered) of the constants in the solution ? If after one week the student remembers 90 percent of the material learned in the semester, and after two weeks remembers 86 percent, how much will she or he remember after summer vacation (about 14 weeks)?
    percent =
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