278 CHAPTER 2 Graphs and Functions 65. Swimming Pool Levels The graph of y = ƒ1x2 represents the amount of water, in thousands of gallons, remaining in a swimming pool after x days. (a) Estimate the initial and final amounts of water contained in the pool. (b) When did the amount of water in the pool remain constant? (c) Approximate ƒ122 and ƒ142. (d) At what rate was water being drained from the pool when 1 … x … 3? 66. Gasoline Usage The graph shows the gallons of gasoline y in the gas tank of a car after x hours. (a) Estimate how much gasoline was in the gas tank when x = 3. (b) When did the car burn gasoline at the greatest rate? 67. Lumber Costs Lumber that is used to frame walls of houses is frequently sold in multiples of 2 ft. If the length of a board is not exactly a multiple of 2 ft, there is often no charge for the additional length. For example, if a board measures at least 8 ft, but less than 10 ft, then the consumer is charged for only 8 ft. (a) Suppose that the cost of lumber is $0.80 every 2 ft. Find a formula for a function ƒ that computes the cost of a board x feet long for 6 … x … 18. (b) Determine the costs of boards with lengths of 8.5 ft and 15.2 ft. 68. Snow Depth The snow depth in a particular location varies throughout the winter. In a typical winter, the snow depth in inches might be approximated by the following function. ƒ1x2 = • 6.5x -5.5x + 48 -30x + 195 if 0 … x … 4 if 4 6x … 6 if 6 6x … 6.5 Here, x represents the time in months with x = 0 representing the beginning of October, x = 1 representing the beginning of November, and so on. (a) Graph y = ƒ1x2. (b) In what month is the snow deepest? What is the deepest snow depth? (c) In what months does the snow begin and end? (d) What is the snow depth at the beginning of April? 0 1 2 3 4 5 x y Time (in days) Gallons (in thousands) 10 20 30 40 50 Water in a Swimming Pool y = f(x) 0 1 2 3 4 5 x y Time (in hours) Gasoline (in gallons) 4 8 12 16 20 Gasoline Use
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