Math help

Gold (Au) has a synthetic isotope that is relatively unstable. After 25.5 minutes, a 128-gram sample has decayed to 2 g.

What is the half-life of this isotope?

8.5 minutes

2.25 minutes

1.5 minutes

4.25 minutes

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  1. x = Xi e^-kt
    2 = 128 e^-25.5 k
    0.015625 = e^-25.5 k
    ln 0.015625 = -25.5 k
    -4.15888 = -25.5 k
    k = 0.163
    so
    1 = 2 e^-0.163 t for half life
    0.5 = e^-0.163 t
    ln 0.5 = -0.693 = -0.163 t
    t = 4.25 minutes

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    Damon
  2. 128/2 = (1/2)^6
    So, now you want
    25.5/6 = 4.25

    For a half-life of k minutes, your function is A = P*(1/2)^(t/k)

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    oobleck

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