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Algebra 2 Decay

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You have 20 grams of phosphorus-32 that decays 5% per day. How long will it take for hlaf of the original amount to decay?

  • Algebra 2 Decay -

    This may not be the math process you want. From a chemists standpoint, I would do the following.
    ln(No/N) = kt. We must determine k.
    So at zero time we start with 20 g. At the end of 1 day we have 20g-5% = 19 g. Plug that into the first order equation of ln(20/19) = k(1 day)
    k = 0.0513
    Then ln(20/10) = 0.0513(t)
    Solve for t. If I didn't goof that is
    13.51 days which I would round to 13.5 days.

  • Algebra 2 Decay -

    Using the "continuous" decay formula, I got

    .5 = 1(e^(-.05t) )
    ln .5 - -.05t lne, but ln e = 1
    t = -.05/ln .5 = .072134.. years
    = 26.3 days

  • Algebra 2 Decay -

    I looked up the half life of P-32. It is 14.28 days. I suspect 5% decay in the problem is just a close number.

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