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Laplace Transform Question.

  1. Oct 14, 2007 #1
    I need to find the Laplace transform of the function below.

    [tex]2\,tu \left( t \right) +5\,{e^{-3\,t+6}}u \left( t-2 \right)[/tex]

    The answer in the back of the book is the following.
    [tex]2\,{s}^{-2}+5\,{\frac {{e^{-2\,s}}}{s+3}}[/tex]

    I understand how the first term was arrived at, but the second term is confusing me.
    From the rules of exponents, when you multiply exponents you add them. So I can rewrite the second term like this [tex]5e^{-3t}e^6*u(t-2)[/tex]

    Now, shouldn't the constants of 5 and [tex] e^6[/tex] become multipliers now? If this is so why don't they appear like that in the final answer?

    Any Ideas why [tex]e^6[/tex] does not appear in the final answer?
    Last edited: Oct 15, 2007
  2. jcsd
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