xn+1= 0.85xn+75
explain thanks
Just, try for several iteration, and you will get the general form.
$\displaystyle x_1=0.85 x_0 + 75 $
$\displaystyle x_2=0.85 x_1 + 75 =0.85^2 x_0 + 75 (0.85) + 75$
$\displaystyle x_3=0.85 x_2 + 75 =0.85^3 x_0 + 75(0.85^2+0.85 + 1)$
$\displaystyle x_4=0.85 x_3 + 75 =0.85^4 x_0 + 75(0.85^3+0.85^2+0.85+1)$
$\displaystyle \vdots$
$\displaystyle x_n=0.85 x_{n-1} + 75 = 0.85^n x_0 + 75 (0.85^{n-1} + \dots + 1)$
$\displaystyle x_n=0.85^n x_0 + 75 \frac{1-0.85^n}{1-0.85}$
Don't forget the steady state solution.