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Math

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The half-life of carbon-14, which is used in dating archaeological finds, is 5730 yr. Assume that 100% of the carbon-14 is present at time 0 yr, or x=0. Write the equation that expresses the percentage of carbon-14 remaining as a function of time.

  • Math - ,

    Amount left = (1/2)^(x/5730)

    check:
    if x = 0 , amount left = (1/2)^0 = 1 = 100%

    if x = 5730 , amount left = (1/2)^(1) = 1/2 = 50%

    formula is good!

  • Math - ,

    Thanks so much!
    Could you tell me the base formula used for that?

  • Math - ,

    normally I would have used \
    amount = a(e^(kt)) where a is the initial amount, in your case it was 1 for 100%
    and k is some constant.

    but since they were talking about "half-life" I used 1/2 as the base

    for half-life questions,
    amount = a(1/2)^(t/half-life period)

    in your case
    amount = 1(1/2)^(t/5730)

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