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Calculuc

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How do you set up this problem?

The decay constant for the radioactive element cesium 137 is .023 when time is measured in years. Find its half-life.

  • Calculuc -

    e^(-0.023t) = 0.5
    Take natural log of both sides.

    -0.023 t = -0.6932
    t = 30 years

  • Calculuc -

    If you are using the standard decay function equation

    amount = initial amount e^-kt, where k = .023 then

    .5 = e^ -.023t
    -.023t = ln .5
    t = ln .5/-.023 = 30.14 years

    check: pick 500 grams
    amount = 500 e^(-.023(30.14))
    = 500 e^ -.69314..
    = 250
    YUP!!!

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