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Basic exponential ln question

  1. Jan 21, 2014 #1
    Doing some self prep for Diff EQ starting next week.

    Determine the decay rate of C14 which has a 1/2 life of 5230. Using e^kt as a function,
    I solve using k5230=ln.5 which gives the obvious answer of negative what I want. How do I know to use the reciprocal (ln2) other than to "just know" I want the positive k value? What if I'm looking for something where I may want a negative but don't know it? Will there be such an instance?

    -thx
     
  2. jcsd
  3. Jan 21, 2014 #2

    BruceW

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    trust your answer bro. if your function is e^kt then you do want k to be negative. A nice way to check is to think about the graph of e^kt and what it looks like for k negative and k positive. And keep in mind the question is about decay, so then which graph makes most sense?
     
  4. Jan 21, 2014 #3

    Ray Vickson

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    Your intuition is off. You either want ##e^{kt}## with ##k < 0## or ##e^{-kt}## with ##k > 0##.The quantity ##Q = Q(t)## of C14 must be a decreasing function of t, since the substance is decaying. If you had ##Q = e^{kt}## with ##k > 0## then Q would be increasing without bound, so the amount of C14 would grow so much over a long time as to swallow up the whole earth---not what you want.
     
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