Let n be the integer index of a year for simulating an endowed (interest earning, scholarship account where x[n] is the amount deposited into the account during year n, and q[n] 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 z-domain c.) Find the transfer function, and zeros for the system. (2), for the system. Find the values of all poles d.) If $1000 is donated every year beginning with year n = 0, find a closed form expression for x[n] 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? Let n be the integer index of a year for simulating an endowed (interest earning, scholarship account where x[n] is the amount deposited into the account during year n, and q[n] 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 z-domain c.) Find the transfer function, and zeros for the system. (2), for the system. Find the values of all poles d.) If $1000 is donated every year beginning with year n = 0, find a closed form expression for x[n] 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