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Math Help - Radioactive Decay

  1. #1
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    Question Radioactive Decay

    In the formula A=Ie^kt, A is the amount of radioactive material remaining from an initial amount I at a given time t, and k is the negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 52% of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.) (Round to the nearest year)

    If some one could please help i need this as soon as possible !!! URGENT!
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  2. #2
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    Quote Originally Posted by lollipopgang
    In the formula A=Ie^kt, A is the amount of radioactive material remaining from an initial amount I at a given time t, and k is the negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 52% of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.) (Round to the nearest year)

    A = I e^(kt) ----------(i)
    A/I = e^(kt)
    ln(A/I) = ln[e^(kt)]
    ln(A/I) = (kt)ln(e)
    ln(A/I) = kt ------------(ii)

    (ii) and (i) are the same.

    ----------
    "(carbon-14 decays at the rate of 0.0125% annually)"

    So, if, say, one year ago, the carbon-14 content is x, then at present, after the 0.0125% decay, the new carbon-14 content is
    ((100 -0.0125)% =) 99.9875% of x.

    Plugging those into (ii),
    ln[(99.9875% of x) /x] = k(1) ------one year past, remember.
    ln(99.9875%) = k
    k = ln(0.999875) = -0.000125008

    (Umm...., really? That is -0.0125%)

    -------------
    " An artifact is discovered at a certain site. If it has 52% of the carbon-14 it originally contained, what is the approximate age of the artifact? "

    If the artifact had y-amount of carbon-14 initially t-years ago, now it has 52% of y.

    ln(A/I) = kt
    ln[(52% of y) /y] = (-0.000125008)t
    ln(0.52) = (-0.000125008)t
    t = ln(0.52) /(-0.000125008)
    t = 5231 years

    Therefore, the artifact is about 5,231 years old. -----answer.
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  3. #3
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    Thanks

    hey thank you very much!! that really help ty
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