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Can this be turned into a differential equation? Recursive diffy Q?

  1. Apr 29, 2012 #1
    Let's say you have a loss of 3% of the current energy on a device for every time is gets turned on. It starts at a 100% energy.

    The only way I could think of it is a recursive function. Here's what I came up:

    E(t) = Et - .03*Et-1

    E(0) = 1

    E(1) = 1 - .03*E0

    E(2) = E1 - .03*E1


    Where E = Energy and t = each time turned on.

    I feel like the solution should be something close to E-.03t but it's not. I know the recursive function describes it exactly but I have to wonder if it's even possible to turn this into a differential equation?

  2. jcsd
  3. Apr 30, 2012 #2
    I don't think so considering you are look at specifc steps(each time you turn it on and off) and not a continuous interval..
  4. Apr 30, 2012 #3


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    Let me propose an alternative recursive formula (it should be obvious why this is the same)
    E1 = .97 E0=.97
    E2 = .97 E1=.972
  5. Apr 30, 2012 #4
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