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Tin decay using separable equ's

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data
    A tin organ pipe decays with age as a result of a chemical reaction that is catalyzed by the decayed tin. as a result, the rate at which the tin decays is proportional to the product of the amount of tin left and the amount that has already decayed. Let M be the total amount of tin left before any has decayed. Find the amount of decayed tin p(t).


    2. Relevant equations
    "Find the amount of decayed tin p(t)." → p(t)=decayed tin,

    "Let M be the total amount of tin left before any has decayed." → amount of tin left=M-p(t)?


    3. The attempt at a solution
    "the rate at which the tin decays is proportional to the product of the amount of tin left and the amount that has already decayed." → dp/dtαM-p(t)αp(t)

    I am not sure if my interpretation of the data is correct. or if it is, i do not know what to do with it to get an equation for p(t). please help!!
     
  2. jcsd
  3. Dec 2, 2009 #2

    kuruman

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    Let q(t) = amount of tin left. Then
    M-q(t) = amount of tin decayed and
    q(t)*(M-q(t))=product of amount left and amount already decayed.

    Can you write a differential equation saying "the rate at which the tin decays is proportional to the product of the amount of tin left and the amount that has already decayed"?
     
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