2. Roy is a merchant frOm medieval England who raises sheep. Every year, he goes to the market in Order to trade wool from his sheep for both timber and grain. Let t = T(w) be the amount of timber, in pounds, that Roy can obtain by trading w pounds of wool, and let 9 = G(w) be the amount of grain, in pounds, that Roy can obtain by trading 12} pounds of wool. Both T(w) and G(w) are invertible, and some values of T('w) and G(w) are listed in the table below. -n-----m \"III-Ian\" (a) What is the average rate of change of T(w) from w = 31 to w = 52? (b) What is the average rate of change of T'1(t) from t = 25 to t = 31? (0) Estimate G" (35), and give a practical interpretation of your answer. ((1) Estimate (G'1)' (58), and give a practical interpretation of your answer. (e) Write an equation for the following in terms of G, T, their inverses, and / or their derivatives: i. Roy can trade 80 pounds of wool for 48 pounds of timber. ii. The amount of wool Roy needs for 35 pounds of timber could also be traded for 75 pounds of grain. iii. By trading 62.4 pounds of wool, Roy can obtain approximately 0.8 more pounds of timber than he could by trading 62 pounds of wool. iv. If Roy wants to trade for 75 pounds of grain instead of 74 pounds, he needs approximately 1.2 additional pounds of wool