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How could I make an exponential function which has a limit of around 1.53?

  1. Nov 8, 2014 #1
    I'm modelling a variable output Y which has a value of 1 at x=0.

    I've noticed that in the system I'm modelling, as x increases, y increases at an exponentially decreasing rate, up until a limit of around 1.53. I view this as changes in x causing the Y value to increase by a max of 53%.

    The only problem is I've been working at it but I don't know where to begin in modelling a function with such a limit.

    Can anyone think of a solution?

    Thanks!
     
  2. jcsd
  3. Nov 8, 2014 #2
    You could use something like y = 1.53 - 0.53/(a*x+1), where a >= 0. I'm assuming x >= 0 as well here.

    Adjust a to determine how quickly it approaches 1.53, for example determine the x at which y is say 1.35 (2/3rds), in which case a = 2/x.
     
  4. Nov 8, 2014 #3
    Good solution, Thanks!
     
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