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8 October, 20:02

You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 5 days later you determine that it has decayed down to 0.6 grams. What is its half-life? (Round your answer to three significant digits.)

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  1. 8 October, 20:26
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    The remaining mass mass of the substance at time t can be modeled with an exponential equation in this form:

    m = ab^t,

    where m is the remaining mass in grams, and t is the time in days.

    We are given the mass at time zero and at time two.

    Let t = 0.

    10 = ab^0

    a = 10

    m = 10b^y

    Let t = 2.

    7 = 10b²

    b² = 0.7

    b ≈ 0.84

    m ≈ 10 (0.84) ^t

    Now to find the half-life, let m = 5 g, which is half of the initial mass. Solve for t.

    5 = 10 (0.84) ^t

    (0.84) ^t = 0.5

    t ln (0.84) = ln (0.5)

    t = ln (0.5) / ln (0.84) ≈ 3.9 days
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