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Math Help - Solving an exponential equation for t.

  1. #1
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    Makurdi
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    Solving an exponential equation for t.

    Carbon-14 is a radioactive isotope of carbon which has a half-life of about 5600 years. Let R be the nearly constant ratio of corbon-12 found in the atmosphere. Let r be the ratio of carbon-14 to carbon-12 found in an observed specimen. It has been shown for carbon-14 dating of objects that
    R = re (tIn4/5600) Where t is the age of the object in years. Suppose a specimen has been found in which
    r = 0.2R, find the age of the specimen
    Last edited by mr fantastic; June 18th 2010 at 04:05 PM.
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  2. #2
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    Hello, blenyo!

    Carbon-14 is a radioactive isotope of carbon which has a half-life of about 5600 years.
    Let R be the nearly constant ratio of corbon-12 found in the atmosphere.
    Let r be the ratio of carbon-14 to carbon-12 found in an observed specimen.
    It has been shown for carbon-14 dating of objects that: .R = re^[(t ln4)/5600]
    . . where t is the age of the object in years.

    Suppose a specimen has been found in which r = 0.2R
    Find the age of the specimen.

    We have: .R/r = e^[(t ln4)/5600]

    We are given: .r = 0.2R . . R/r = 5


    Hence: .e^[(t ln4)/5600] .= .5

    . a . . . . . . .(t ln4)/5600 .= .ln5

    . n . . . . . . . . . . . . . . t .= .(5600 ln5)/(ln4)


    Therefore: .t . .6501.4 years.

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  3. #3
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    By the way, the natural logarithm is ln(x), not In(x)!
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