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March 28, 2017

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half life carbon -14 is 5,730 years. If you start out 50 grams, how long will it take until it reaches 2 grams?

  • Algebra 2 - ,

    x = Xi e^-kt
    x/Xi = .5 = e^-5730 k
    ln .5 = -5730 k
    -.69315 = -5730 k
    k = 1.21*10^-4

    x = Xi e^-1.21*10^-4 t
    2 = 50 e^-1.21*10^-4 t
    .04 = e^-1.21*10^-4 t
    ln .04 = -1.21*10^-4 t
    -3.22 = -1.21*10^-4 t
    2.66 * 10^4
    = 26,600 years

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