Board Price Problem: If you check the prices of various lengths of lumber, you will find

Chapter 1, Problem 2

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Board Price Problem: If you check the prices of various lengths of lumber, you will find that a board twice as long as another of the same type does not necessarily cost twice as much. Let x be the length, in feet, of a 2 6 board (Figure 1-1e) and let y be the price, in cents, that you pay for the board. Assume that y is given by y = 0.2x3 4.8x2 + 80x x 6 2 2-by-6 Figure 1-1e a. Find the price of 2 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 x = 5 to 5.1, x = 5 to 5.01, and x = 5 to 5.001. c. The average number of cents per foot in part b 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? d. Estimate the instantaneous rate of change in price if x is 10 ft and if x is 20 ft. You should find 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 show that this principle does not apply to buying longer boards. Think of a reason why it does not apply.