Question: 2. (20 Marks) Are the following two dynamic systems (a) (t+1 = 22+ + 4; and (b) 3x4+1 = Xt + 2 globally asymptotically stable?

2. (20 Marks) Are the following two dynamic systems (a) (t+1

2. (20 Marks) Are the following two dynamic systems (a) (t+1 = 22+ + 4; and (b) 3x4+1 = Xt + 2 globally asymptotically stable? Why or why not? 3. (20 Marks) Suppose that at time t = 0, you borrow $100000 at a fixed interest rate r of 7% per year. You are supposed to repay the loan in 30 equal annual repayments so that after n = 30 years, the mortgage is paid off. How much is each repayment? Don't directly use the formula. Please derive the difference equation for the outstanding balances and find the general solution then. 2. (20 Marks) Are the following two dynamic systems (a) (t+1 = 22+ + 4; and (b) 3x4+1 = Xt + 2 globally asymptotically stable? Why or why not? 3. (20 Marks) Suppose that at time t = 0, you borrow $100000 at a fixed interest rate r of 7% per year. You are supposed to repay the loan in 30 equal annual repayments so that after n = 30 years, the mortgage is paid off. How much is each repayment? Don't directly use the formula. Please derive the difference equation for the outstanding balances and find the general solution then

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