Math

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The half-life of radioactive strontium-90 is approximately 32 years. In 1961, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 8 percent of the original amount absorbed remains?

  • Math -

    Since 1/8 = (1/2)^3, it will take 3 half-lives, or 96 years.

  • Math -

    I would say
    .08 = (1/2)^(t/32)
    ln .08 = (t/32) ln .5
    t/32 = ln .08/ln .5 = 3.6438..
    t = 116.6 years

    rough check:
    after 32 years --- 50% left
    after 64 years --- 25% left
    after 96 years --- 12.5% left , (which is 1/8 but not 8%)
    after about 16 more years we would lose about 1/4 of what was left, leaving appr 3/4 of 12.5 or appr 9%

    answer is quite plausible

  • math - oops -

    ouch. How did I read 8% as 1/8?

    As usual, go with Reiny's answer!

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