Suppose that you deposit $1,050 each week into a special savings account. The bank takes 4%...

 

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Suppose that you deposit $1,050 each week into a special savings account. The bank takes 4% from your total savings for service fees just before you make a deposit. A discrete-time dynamical system modelling this situation is n+1 = 0.96x + 1,050 a) If you initially have $1,600 in the bank, how much money will you have at the end of the third week? Give your answer with an accuracy of two decimal places. Answer: b) Write down the updating function of the dynamical system. Answer: f(x)= c) Find the equilibrium point of the dynamical system. Give exact an value; do not round. Answer: d) Give the solution of the dynamical system with x0 = 1.600. Answer: X= e) Draw cobweb diagrams of the dynamical system with various initial conditions, and interpret these to decide if this dynamical system has a stable equilibrium point: (a) Yes, the equilibrium point is stable. (b) No, the equilibrium point is unstable. Suppose that you deposit $1,050 each week into a special savings account. The bank takes 4% from your total savings for service fees just before you make a deposit. A discrete-time dynamical system modelling this situation is n+1 = 0.96x + 1,050 a) If you initially have $1,600 in the bank, how much money will you have at the end of the third week? Give your answer with an accuracy of two decimal places. Answer: b) Write down the updating function of the dynamical system. Answer: f(x)= c) Find the equilibrium point of the dynamical system. Give exact an value; do not round. Answer: d) Give the solution of the dynamical system with x0 = 1.600. Answer: X= e) Draw cobweb diagrams of the dynamical system with various initial conditions, and interpret these to decide if this dynamical system has a stable equilibrium point: (a) Yes, the equilibrium point is stable. (b) No, the equilibrium point is unstable.