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Math Help - Half-life

  1. #1
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    Half-life

    In the skull of an animal found in an archaeological dig, it was determined that about 20% of the original amount of carbon-14 was still present. If the half-life of carbon-14 is 5730 years, find the approximate age of the animal.
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  2. #2
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    Quote Originally Posted by mikegar813 View Post
    In the skull of an animal found in an archaeological dig, it was determined that about 20% of the original amount of carbon-14 was still present. If the half-life of carbon-14 is 5730 years, find the approximate age of the animal.
    y = y_0 \left(\frac{1}{2}\right)^{\frac{t}{5730}}

     <br />
0.2 = \left(\frac{1}{2}\right)^{\frac{t}{5730}}<br />

    solve for t
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  3. #3
    MHF Contributor Calculus26's Avatar
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    Let Q(t) denote the amount of C-14

    For all half-life prblms

    Q(t) = Q(0) e^(-kt)

    Where k = ln(2)/halflife

    in your prblm

    k= ln(2)/5730 = .00012

    Q(t) = Q(0) e^(-.00012t)

    solve Q(t) = .2Q(0) = Q(0) e^(-.00012t) for t

    .2 = e^(-.00012t)

    I'll let you finish
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  4. #4
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    i got 13304.6 years does this sound right?

    t= (-5730(ln 0.2))/(ln 2)
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  5. #5
    MHF Contributor Calculus26's Avatar
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    yes but in reality you wouldn't claim that much accuracy--It would probably be claimed as about 13,000 years
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