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Radioactive Decay Graph in y=mx+c form

  1. Feb 13, 2010 #1
    1. The problem statement, all variables and given/known data

    This is an equation relating radioactivity of lead in marine core sediments in comparison with the depth of the sediment.

    The equation is AL=A0exponential - λL/s

    Where AL = activity at depth L (Bqkg-1)
    Where A0 = activity at depth 0 cm (Bqkg-1)
    λ = decay constant 0.031 yr-1
    L= sediment depth (cm)
    s= sediment accumulation rate (cmyr-1)

    I need to make this into y=mx+C form

    2. Relevant equations

    As above.

    3. The attempt at a solution

    Well Ln both sides gives me

    Ln AL = Ln (A0exponential - λL/s)

    Ln AL = (Ln A0) + (Ln*exponential - λL/s) (which cancels)

    Ln AL = (Ln A0) - λL/s

    Ln AL = y
    Ln (A0) = c
    L= x
    1/s = m

    Is that correct? The graph has to be Ln AL against L but I wasn't sure about m and c. Thanks :)
  2. jcsd
  3. Feb 13, 2010 #2
    Hello Rockerjabroni your equation is correct.If you now compare this to y=mx+c you should see that the graph has a negative slope of gradient lambda/s and intercept lnAzero.
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