338 CHAPTER 3 Polynomial and Rational Functions (Modeling) Solve each problem. See Example 6. 73. Debit Card Transactions The table shows the number of transactions, in billions, by users of bank debit cards for selected years. The data are modeled by the quadratic function ƒ1x2 = 0.0553x2 + 2.62x + 7.90, where x = 0 corresponds to the year 2000 and ƒ1x2 is the number of debit card transactions in billions. If this model continues to apply, what will be the number of debit card transactions in 2022? Round to the nearest tenth of a billion. 74. Concentration of Atmospheric CO2 The quadratic function ƒ1x2 = 0.0139x2 + 0.766x + 317 models the worldwide atmospheric concentration of carbon dioxide in parts per million (ppm) over the period 1960–2018, where x = 0 represents the year 1960. If this model continues to apply, what will be the atmospheric CO2 concentration in 2025? Round to the nearest unit. (Data from U.S. Department of Energy.) 75. Minimum Food Truck Cost Daily costs for a food truck business that sells pizza by the slice are approximated by the quadratic function C1x2 = 0.00128x2 - 0.64x + 200, where C1x2 is the cost, in dollars, to sell x slices of pizza. Find the number of slices of pizza that should be sold to minimize the cost. What is the minimum cost? 76. Accident Rate According to data from the National Highway Traffic Safety Administration, the accident rate as a function of the age of the driver in years x can be approximated by the quadratic function ƒ1x2 = 0.0232x2 - 2.28x + 60.0, for 16 … x … 85. Find both the age at which the accident rate is a minimum and the minimum rate to the nearest hundredth. Year Transactions (in billions) 2000 8.3 2003 15.6 2006 25.0 2009 37.5 2012 47.3 2015 59.0 2016 63.0 2017 69.6 Data from Federal Reserve System. 77. College Enrollment The table lists total fall enrollments in degree-granting postsecondary colleges in the United States for selected years. (a) Plot the data. Let x = 0 correspond to the year 2000. (b) Find a quadratic function ƒ1x2 = ax2 + bx + c that models the data. (c) Plot the data together with ƒ in the same window. How well does ƒ model enrollment? (d) Use ƒ to estimate total enrollment in 2018 to the nearest tenth of a million. Year Enrollment (in millions) 2000 15.3 2004 17.3 2008 19.1 2012 20.6 2016 19.8 Data from National Center for Education Statistics.
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