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Math Help - Application of 1st order differential equations 2

  1. #1
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    Application of 1st order differential equations 2

    The decaying rate of radium is directly proportional to its access mass.
    a) Write a differential equation to relate mass of radium, x and time t.
    b) If it takes 1400 years for a sample to lose half of its initial mass, how long does it take to lose 1% of the initial mass?

    For question a) x=A(e^-kt) A=e^c

    For question b) My problem was the initial mass...actually how to do this type of question??(IF mass was not given)
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  2. #2
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    Quote Originally Posted by sanikui View Post
    The decaying rate of radium is directly proportional to its access mass.
    a) Write a differential equation to relate mass of radium, x and time t.
    b) If it takes 1400 years for a sample to lose half of its initial mass, how long does it take to lose 1% of the initial mass?

    For question a) x=A(e^-kt) A=e^c

    For question b) My problem was the initial mass...actually how to do this type of question??(IF mass was not given)
    Actually the differential equation is \frac{dP}{dt} = - k P,\;P(0)=A which you give the solution P = Ae^{-kt}. The half life is 1400 yrs so P(1400) = Ae^{-1400k} = \frac{A}{2} from which you can solve for k (the A's cancel). Then find t* such that P(t^*) = Ae^{-kt*} = .99A (again the A's cancel).
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