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precal

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If the half-life of a certain radioactive substance is 2000 years, estimate how many years must elapse before only 35% of the radioactive substance remains?

  • precal - ,

    For half-life question, a good equation to use is

    amount = starting value (1/2)^(t/k) where k is the half-life

    so :
    .35 = 1(1/2)^(t/2000) , t in years
    .35 = (.5)^(t/2000
    log .35 = log ( (.5)^(t/2000)
    log .35 = (t/2000) log .5
    t/2000 = log .35/log .5
    t = 2000( log .35/log .5) = 3029.14

    it would take appr 3029 years

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