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Math Help - Updating function problem. What is the solution of the dynamical system at x0=200?

  1. #1
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    Updating function problem. What is the solution of the dynamical system at x0=200?

    xn+1= 0.85xn+75
    explain thanks
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  2. #2
    Junior Member erich22's Avatar
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    Re: Updating function problem. What is the solution of the dynamical system at x0=200

    Just, try for several iteration, and you will get the general form.
    x_1=0.85 x_0 + 75
    x_2=0.85 x_1 + 75 =0.85^2 x_0 + 75 (0.85) + 75
    x_3=0.85 x_2 + 75 =0.85^3 x_0 + 75(0.85^2+0.85 + 1)
    x_4=0.85 x_3 + 75 =0.85^4 x_0 + 75(0.85^3+0.85^2+0.85+1)
    \vdots
    x_n=0.85 x_{n-1} + 75 = 0.85^n x_0 + 75 (0.85^{n-1} + \dots + 1)
    x_n=0.85^n x_0 + 75 \frac{1-0.85^n}{1-0.85}
    Don't forget the steady state solution.
    Last edited by erich22; March 31st 2015 at 06:39 PM.
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