Instructions: the exam is closed book and closed notes. You may use an approved calculator, but be sure to show your work on each problem for full credit. Work that is crossed out or erased will not be graded. Turn in any scratch paper that you use during the exam. You will have one hour and 45 minutes to work on the exam. You do not need to simplify your answer. 2: (14 points) consider the following discrete-time dynamical system: (a) find the equilibria algebraically. xt+1 = x2 t + 7xt + 8 (b) apply the stability test/slope criterion to each of the equilibria you found in (a). What can you conclude? (c) the updating function is graphed below, along with the diagonal. 3 steps starting from the initial condition x0 = 3. 5. Describe in detail the long-term behavior of this solution.