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College Math

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An artifact was found and tested for its carbon-14 content. If 88% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.

  • College Math -

    If you start with amount P, then after t years, R, the fraction remaining, is

    R = 2^(-t/5730)

    See how that works? Every 5730 years, the power of 2 goes down by 1.

    2^(-t/5730) = .88
    -t/5730 = ln(.88)/ln(2) = −0.321928095
    t = 5730 * 0.321928095
    t = 1844.64798435
    or, to the nearest 100 years, 1800.

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