A really interesting situation occurs for the logistic equation, Equation 4.46 when a = 3.82831 and x1 = 0.51. Show that a three cycle occurs with the approximate x values 0.16, 0.52, and 0.96 for the first 80 cycles before the behavior apparently terns chaotic. Find for what iteration the next apparently periodic cycle occurs and for how many cycles it stays periodic.