1. Discrete systems: Our first example is the famous Logistic example x_{n+1} = lambda x_n ( 1 - x_n) Suppose lambda = 1 and we start with n | x_n 0 | 0.5 1 | 0.25 2 | 0.1875 3 | 0.15234375 4 | 0.12913513513183594 .... This system says the next x_n (read: x subscript n), x_{n+1} is the current x_n * 1 - x_n. Getting the ti89 to compute x_n's. a. Get into sequence mode: MODE Graph->SEQUENCE ENTER ENTER b. Enter the equation. green diamond y= (F1) u1(n) = ENTER and fill in u1(n) = 1*u1(n-1)*(1-u1(n-1)) Comment, this is the same equation shifted down one. This is a recursive definition so we have to fill ui1 = 0.5 green diamond graph (F3) green diamond WINDOW (F2) We need to set the window. Try ymin = 0 ymax = 1 xmin=0 xmax=100 nmin=10 nmax=100. graph again. Make lambda 3.5 and do it again Look at the data, set the table up green diamond tbSet start at 100, and delta 1. green data TABLE and wait for it.