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Math Help - Logarithm word problems

  1. #1
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    Logarithm word problems

    1. The doubling period for a colony of bacteria is 5 days. Initially, there are 20 cells in the culture. What is the approximate growth rate per day?

    2. Boris the bone guy finds a rather unusual animal femur buried underneath his porch. Boris did a quick carbon-14 test and determined that 86.2% of the original carbon-14 remained. Approximately how long ago did the unusual animal die?

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  2. #2
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    2. Boris the bone guy finds a rather unusual animal femur buried underneath his porch. Boris did a quick carbon-14 test and determined that 86.2% of the original carbon-14 remained. Approximately how long ago did the unusual animal die?
    Let's say the half-life of Carbon-14 is 5750 years. The decay constant is

    k=\frac{-1}{5750}ln(2)\approx{-.00012055}

    86.2 % remains:

    .862=e^{-.00012055t}

    \frac{ln(.862)}{-.00012055}=t=1231.88 \;\ yrs
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