(30 pts): Let n be the integer index of a year for simulating an endowed interest earning) scholarship account where xn is the amount deposited into the account during year n, and qin is the balance of the account at the end of year n. At the beginning of each new year, the balance is increased by adding 7% interest based on the balance at the end of the previous year. Also at the beginning of each year, 10% of the average of the balances at the end of the two previous years is removed from the account to pay for scholarships. Let y[n represent the amount of scholarship money paid at the beginning of year n. a.) Write a difference equation in standard form. b.) Sketch a flow diagram that represents the zero-state system in the 2-domain. c.) Find the transfer function, H(), for the system. Find the values of all poles and zeros for the system. d.) If $1000 is donated every year beginning with year n = 0, find a closed form expression for en and X(2). e.) Assuming there no money in the account prior to year n = 0, and a deposit formula as specified in part d above, what is the amount paid in scholarships for year n = 3? f.) If the system can reach steady-state with the deposit formula as specified in part d above, find the steady-state annual scholarship amount paid, ya[n]. If the system cannot reach steady-state, briefly explain why it cannot. (30 pts): Let n be the integer index of a year for simulating an endowed interest earning) scholarship account where xn is the amount deposited into the account during year n, and qin is the balance of the account at the end of year n. At the beginning of each new year, the balance is increased by adding 7% interest based on the balance at the end of the previous year. Also at the beginning of each year, 10% of the average of the balances at the end of the two previous years is removed from the account to pay for scholarships. Let y[n represent the amount of scholarship money paid at the beginning of year n. a.) Write a difference equation in standard form. b.) Sketch a flow diagram that represents the zero-state system in the 2-domain. c.) Find the transfer function, H(), for the system. Find the values of all poles and zeros for the system. d.) If $1000 is donated every year beginning with year n = 0, find a closed form expression for en and X(2). e.) Assuming there no money in the account prior to year n = 0, and a deposit formula as specified in part d above, what is the amount paid in scholarships for year n = 3? f.) If the system can reach steady-state with the deposit formula as specified in part d above, find the steady-state annual scholarship amount paid, ya[n]. If the system cannot reach steady-state, briefly explain why it cannot
