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Math Help - applied de involving decay process

  1. #1
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    applied de involving decay process

    A radioactive material, for example the isotope carbon-14, disintegrates at a rate proportional to the amount currently present. Let W(t) be the amount present at time t, measured in days, and r be the proportionality constant, the decay rate.

    (a) Write a differential equation to describe the decay process.
    (b) If 100 mg of carbon-14 decays to 82.04 mg in one week, determine the decay rate, r.
    (c) Find an expression for the amount of carbon-14 present at any time, t.
    (d) Find the time required for the thorium to decay to one-half its original amount.

    i know that the de :

    dW/dt = -k dt

    and W(t) = A e-kt


    but i dunno how to solve (b), (c) and (d)....

    pls help me....
    Last edited by bobey; March 9th 2010 at 12:40 AM.
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  2. #2
    Junior Member
    Joined
    Jul 2009
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    you already solved c)
    W(t) = A e-kt

    you only need to replace A for the initial amount of thorium (if there is one)


    b) is just solving 2 equations
    1st - the initial quantity is 100 W(0)=100
    2nd - the quantity at time t is 82.04 W(....


    d) is solving the equation
    the quantity at time t is A/2
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