Consider a variation on the Taylor rule: r = (0.25)rTAYLOR + (0.75)r(-1), where r is the real

Question:

Consider a variation on the Taylor rule: r = (0.25)rTAYLOR + (0.75)r(-1), where r is the real interest rate in a quarter, rTAYLOR is the interest rate implied by the Taylor rule, and r(-1) is the interest rate in the previous quarter. Call this rule TR-S.
a. Compare the behavior of the interest rate under TR-S to its behavior under the basic Taylor rule. (Hint: What might “S” stand for?)
b. Is TR-S a realistic description of central banks’ behavior? Why might they follow such a rule rather than the basic Taylor rule?