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Math Help - modelling!

  1. #1
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    modelling!

    A radio active element is know to decay at the rate of 2% every 20yrs. If initially you add 165g of the element, how much would you have in 60yrs.
    what is the half life time of the element.

    i formulated the model as

     E_{t+1} = 1.02E_{t} , where t \sim O(20)

     E_{0} = 165g

     t= 0

    solution

     E_{1} = 1.02E_{0}

     t= 3

     E_{4} = 1.02^4 E_{0} = 1.02^4 * 165 (in 60yrs)

    pls cross check to correct me and how do i compute the half life?

    thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: modelling!

    The half-life equation is exponential and continuous so a discrete model isn't going to work here. Read this.

    Now, a 1/2 life is the time it takes for 50% of the material to decay. You know that 2% of your material decays in 20 years. So how much time would it take for 50% to go?

    -Dan
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  3. #3
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    Re: modelling!

    In your answer where you have 1.02 it should be 1/1.02 and in the last line the index should be 3 not 4.
    After n half lives the original mass
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