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Radioactive iodine is used to determine the health of the thyroid gland. It decays according to the equation y=ae -0.0856t where t is in days. Find the half-life of this substance. Round to the tenths place.

  • Alg2 -

    If you can express the amount as

    y = a*2^(-t/n)

    then the half-life is n years. That is, as t increases by n, the amount is multiplied by 1/2

    ae^-.0856t = a*2^(-t/n)
    divide by a and take logs
    -.0856t = -t/n ln 2
    divide by t

    .0856 = ln2/n
    n = ln2/.0856 = .6931/.0856 = 8.1

    So, the half-life is 8.1 days

    check: wikipedia says the half-life is 8.02 days

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