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17 August, 12:29

The amount of carbon-14 present in animal bones t years after the animal's death is given by P (t) = - 0.00012097t. How old is an ivory tusk that has lost 34 % of its carbon-14?

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  1. 17 August, 15:14
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    I believe the equation you gave is wrong because the standard form of equation for C-14 decay is in the form of:

    A = Ao e^-kt

    So I think the right form of equation is (correct me if I’m wrong):

    P (t) = Po e^ (-0.00012097t)

    Where,

    Po = initial value of C-14 at t = 0

    t = time elapsed

    Since it is given that:

    P = (1 - 0.34) Po

    P = 0.66 Po

    Therefore, t is:

    0.66 Po = Po e^ (-0.00012097 t)

    0.66 = e^ (-0.00012097 t)

    taking ln of both side:

    ln 0. 66 = - 0.00012097 t

    t = - ln 0. 66 / 0.00012097

    t = 3,434.86 years

    Therefore the ivory tusk is about 3,435 years old.
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