13. Rolling Tire Problem: A pebble is stuck in t sec y in. the tread of a car tire (Figure 1-2h). As the 1.2 0.63 wheel turns, the distance, y inches, between 1.3 0.54 the pebble and the road at various times, 1.4 0.45 t seconds, is given by the adjacent chart. 1.5 0.34 a. About how fast is y changing at each time? 1.6 0.22 i. t = 1.4 1.7 0.00 ii. t = 1.7 1.8 0.22 iii. t = 1.9 1.9 0.34 b. At what time does the stone strike the 2.0 0.45 pavement? Justify your answer. Figure 1-2h2. Board Price Problem: If you check the prices of various lengths of lumber. you will find that a board twice as long as another 7 of the same type does not necessarily cost twice as much. Let x 5' = 6 be the number of feet long a 2\" x 6" board is (Figure lle) and F"Xfee'" .let y be the number of cents you pay for the board. Assume Figure 1-] e that y is given by . y = 0.22:3 ' 4.8x2 + 80x. , a. Find the price of 2\" x 6" boards that are 5 ft long, 10 ft long, and 20 ft long. b: Find the average rate of change of the price in cents per foot for 5 ft to 5.1 ft. 5 ft to 5.01 ft. and 5 ft to 5.001 ft. ' c. The average number of cents per foot in 2b is approaching an integer as the change in x gets smaller and. smaller. What integer? What is the name given to this rate of change? (1. Estimate the instantaneous rate of change in price if x is 10 ft and if x is 20ft. You should nd that each of these rates is an integer. e. One of the principles of marketing is that when you buy in larger quantities, you usually pay less per unit. Explain how the numbers in Problem 2 show that this principle does not apply to buying longer boards. Think of a reason why it does not apply