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How is this simplification possible?

  1. Sep 16, 2011 #1
    x(t) = (148/3)e^(-6t) + 1

    I am trying to find the amount of salt (x) in the tank at time = 40.

    Out of interest I checked it out on wolframalpha, and
    (148/3)e^(-240) is around 2.67E(-103) SO RIDICULOUSLY SMALL
    but as soon as put the 'plus 1' on the end, it someone all simplifies down to 1?
    How is that possible................? thanks!
     
  2. jcsd
  3. Sep 16, 2011 #2

    hotvette

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    Homework Helper

    One plus a very small number is one. The function starts out at ~50 at t=0 and decreases very rapidly to an asympotic value of 1.
     
  4. Sep 16, 2011 #3
    In addition, computers typically can't handle numbers with that many digits. Rounding has to occur unless you are using a special math library with provision for very long numbers.

    Fred
     
  5. Sep 16, 2011 #4

    pwsnafu

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    To put this into perspective, x(2) = 1.003...
    Which means that unless you go to 4 significant figures or more, you won't see a difference.
    And most experiments in a lab is only 3 significant figures.

    As you have shown, (148/3)e^(-240) only differs from zero in the 102nd decimal place.
    You need to think about why you would ever need precision to that level.
     
  6. Sep 17, 2011 #5

    HallsofIvy

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    Strictly speaking, it does NOT "simplify to 1". It is approximately equal to 1 and, depending on the situation can be treated as 1.
     
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