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1/e Life-Time of a Graph

  1. Sep 4, 2013 #1
    1. The problem statement, all variables and given/known data

    Given that... The units of voltage are “Volts” and the units of time are “seconds”
    Show τe (1/e life-time) on your graph and find a value for τe from your graph. ( The definition of τe is similar to the definition of τ1/2 (half-life))

    V(t) t(s)
    24 0.1
    20 0.2
    14 0.3
    12 0.4
    10 0.5
    7.5 0.6
    5.5 0.7
    4.8 0.8
    3.5 0.9
    2.6 1.0

    2. Relevant equations

    V(t) = Vi*e^-αt

    3. The attempt at a solution
    I got the half life as .3 seconds. But I have no idea what is the life-time of a graph and how to even get it. I've tried googling it but to no avail. If anyone can help tell me the value and how you got it, I would greatly appreciate it. Thanks!
     
  2. jcsd
  3. Sep 4, 2013 #2
    The 1/e lifetime is 1/α. Take the natural log of both sides of the equation. Graph the data using a semi-log scale for V and an arithmetic scale for t. The slope should be -α. See if you can figure out why this procedure works.
     
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