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Math Help - half life question

  1. #1
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    half life question

    I have a math question that I need help with:

    "carbon 14 has a half life of approximately 8000 years. If a sample contains 12.5% carbon 14 and 87.5% carbon 16, how old is the sample?"

    the answer is 24,000 but I can't for the life of me figure out why. any help would be greatly appreciated. thanks.
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  2. #2
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    Re: half life question

    Let us assume we do not know any mathematics. You can still figure it out conceptually. We know that 1/8 of our sample is carbon 14, and 7/8 of it is carbon 16. That is, our sample once has 100% carbon 14. It took 8000 years to go from 100% to 50%. It took another 8000 years to go from 50% to 25%. And finally, it took 8000 years to go from 25% to 12.5%. Three 8000 years, would be 24,000 years. Decay of radioactive material follows an exponential function. Whenever you know the half-life of a substance and the percentage of your sample that substance consists, say x%, you can solve the equation x/100=(1/2)^k for k. Then, you multiply the half-life by k to see how old your sample is. I hope this helped.
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  3. #3
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    Re: half life question

    thanks so much! that helped a lot
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