277 2.6 Graphs of Basic Functions 58. Postage Charges Suppose that the cost of mailing a letter weighing x ounces, where x 70, is ƒ1x2 = 55 - 15Œ1 - xœ cents. (a) What is the cost of mailing a 2.6-ounce letter? (b) What is the cost for the first ounce? (c) What is the cost for each additional ounce or fraction of an ounce? 59. Postage Charges Assume that postage rates are $0.49 for the first ounce, plus $0.21 for each additional ounce, and that each letter carries one $0.49 stamp and as many $0.21 stamps as necessary. Graph the function ƒ that models the number of stamps on a letter weighing x ounces over the interval 10, 54. 60. Parking Charges The cost of parking a car at an hourly parking lot is $3 for the first half-hour and $2 for each additional half-hour or fraction of a half-hour. Graph the function ƒ that models the cost of parking a car for x hours over the interval 10, 24. 61. Water in a Tank Sketch a graph that depicts the amount of water in a 100-gal tank. The tank is initially empty and then filled at a rate of 5 gal per minute. Immediately after it is full, a pump is used to empty the tank at 2 gal per minute. 62. Distance from Home Sketch a graph showing the distance a person is from home after x hours if he or she drives on a straight road at 40 mph to a park 20 mi away, remains at the park for 2 hr, and then returns home at a speed of 20 mph. 63. New Truck Market Share The new vehicle market share (in percent) in the United States for trucks is shown in the graph. Let x = 0 represent 2010, x = 1 represent 2011, and so on. 2010 2011 Year 2017 40 0 Percent 50 60 70 2012 2013 2014 2015 2016 Data from U.S. Bureau of Economic Analysis. Truck Market Share x y (0, 48.1) (4, 51.9) (7, 63.0) (a) Use the points on the graph to write equations for the graphs in the intervals 30, 44 and 14, 74. (b) Define this graph as a piecewise-defined function ƒ. 64. Flow Rates A water tank has an inlet pipe with a flow rate of 5 gal per minute and an outlet pipe with a flow rate of 3 gal per minute. A pipe can be either closed or completely open. The graph shows the number of gallons of water in the tank after x minutes. Use the concept of slope to interpret each piece of this graph. 0 2 4 6 8 10 4 8 12 16 20 24 x y (3, 15) (5, 19) (8, 19) (10, 13) Time (in minutes) Water (in gallons) Water in a Tank
RkJQdWJsaXNoZXIy NjM5ODQ=