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Math Help - Exponential Integration question

  1. #1
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    Exponential Integration question



    For question 15, so far, I have got the following

    dN/N = -k dt

    From there, I get N(0)e-kt

    I solved k to be 0.0001216 that was using k = -ln(1/2)/5700 ==> (ln 2)/5700
    then N(t) = N(0)e-(ln 2)t/5700
    which is also N(t) = N(0)*-2t/5700

    So I am getting close, but what is N(0)?
    so to do the part b I solve N(t) = N(0)*-20.4(5700) - but what is N(0)?



    Question 16 I have solved, don't have any issues with that.
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  2. #2
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    Re: Exponential Integration question

    There is a little mistake in the indices of the equation you derived, you brought back the minus sign after changing -ln(1/2) to ln(2) so the equation is
    N(0)e^{\frac{ln(2)t}{5700}}

    The 40% is related to number of atoms not time, if it decays to 40% of its original size after a time T then 0.4*N(0)= N(T)
    Using the equation you derived,

    0.4N(0)=N(0)e^{\frac{ln(2)T}{5700}}

    The N(0) cancels on both sides.
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