math

Carbon 14 (14C) dating assumes that the carbon dioxide on Earth today has the same radioactive content as it did centuries ago. If this is true, the amount of 14C absorbed by a tree that grew several centuries ago should be the same as the amount of 14C absorbed by a tree growing today. A piece of ancient charcoal contains only 17% as much radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal given that the half-life of 14C is 5700 years? (Round your answer to the nearest whole number.)

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  1. the amount remaining as a fraction of the original amount after t years is

    (1/2)^(t/5700)

    So, you need to solve

    (1/2)^(t/5700) = 0.17
    t/5700 log(1/2) = log(0.17)
    t = 5700 log(0.17)/log(0.50) = 5700*2.55 = 14571

    note that 17% is about 1/6, so you expect a number between 2 and 3 half-lives

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