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Math Help - O.D.E

  1. #1
    Junior Member
    Joined
    Feb 2009
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    28

    O.D.E

    The half-life of Thorium 230 is about 75000 years, while that of Uranium 234 is about 245000 years.
    Suppose the decay rate per atom of Uranium 234, originally assumed to be a constant kU, actually *decreases*
    slowly throughout the history of the Universe, according to the rule
    kU(t) = a/(1 + t/b)^2 ;
    where t ranges from zero [when Uranium 234 was first created] to infinity, and where a and b are
    constants [with what units?] which we can claim to know. If Uo was the initial number of Uranium 234 atoms in a given object, how many atoms of Uranium 234 will there be as t tends to infinity?

    dU/dt = -kU = -a/(1 + t/b)^2
    after integrate and subsitute the value of Uo, i got
    U=ab^2/(b+t)+Uo-ab
    when t tends to infinity, U=Uo

    Is my solution correct?
    Last edited by elliotyang; February 3rd 2009 at 06:30 AM.
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