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Math Help - Hi, may I ask about exponential decay?

  1. #1
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    Hi, may I ask about exponential decay?

    Hi, all. Please teach me a question about exponential decay.

    The question is "You buy a supposedly genuine 2000 year old eggshell of the extinct giant elephant bird Aepyornis, however you are not sure of its authenticity. You useyour Liquid Scintillation Counter to work out that the proportion of carbon-14, C14, in a sample of the eggshell is 0:883% of the proportion that would naturally occur at the time it was laid. Using methods from the notes, make a decision whether the eggshell authentic or not. The decay constant of C14 is r= 0.000125 per year."

    I solved this by using M/M0 = e^rt, and r = 0.000125. So, e^(-0.000125*2000) = 0.778801....

    C14 decreases as time increases. But, 0.883%, in other words, approximately 0.00883 of the eggshell was C14 as naturally occured.
    If the eggshell is authentic, that means that the proportion of C14 has increased which yield contradiction. Thus, the eggshell is not authentic.

    May I ask if I am correct?
    Thanks a lot!
    Have a great day.
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  2. #2
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    Re: Hi, may I ask about exponential decay?

    You are correct, but the c14 hasn't "increased", it just hasn't decayed enough to be 2000 years old.

    A yield of .883% is greater than the expected .771%, which means the egg is not authentic.

    To find out how old the egg is, solve the equation e^(-0.000125 * x) = .883
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  3. #3
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    Re: Hi, may I ask about exponential decay?

    Quote Originally Posted by SedSerd View Post
    You are correct, but the c14 hasn't "increased", it just hasn't decayed enough to be 2000 years old.

    A yield of .883% is greater than the expected .771%, which means the egg is not authentic.

    To find out how old the egg is, solve the equation e^(-0.000125 * x) = .883
    I deeply appreciate your help.
    May I ask if 0.778 is a percentage? I thought it would be 77.8%.
    So, I thought to find out how old the egg is, I need to solve the equation e^(-0/000125 * x) = 0.0083...
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