152 CHAPTER 1 Equations and Inequalities (a) According to the model, what would emissions be in 2018? Round to the nearest tenth of a million metric tons. (b) Find the nearest year beyond 2012 for which this model predicts that emissions will reach 3800 million metric tons. 54. Cost of Public Colleges The average cost, in dollars, for tuition and fees for in-state students at four-year public colleges over the period 2008–2018 can be modeled by the equation y = -28.75x2 + 532.0x + 7734, where x = 0 corresponds to 2008, x = 1 corresponds to 2009, and so on. Based on this model, for what year before 2018 was the average cost $9500? (Data from The College Board, Annual Survey of Colleges.) 55. e-Commerce Revenue Estimated e-commerce revenue from employers in the United States during the years 2011 through 2016 can be modeled by the equation y = 1.982x2 + 36.26x + 380.2, where x = 0 corresponds to 2011, x = 1 corresponds to 2012, and so on, and y is in billions of dollars. Approximate the e-commerce revenue from these employers in 2016 to the nearest billion dollars. (Data from U.S. Census Bureau.) 56. Cable’s Top Internet Speeds The top cable Internet speeds during the years 2007 through 2018 can be modeled by the equation y = 15.89x2 + 11.33x - 19.05, where x = 0 corresponds to 2007, x = 1 corresponds to 2008, and so on, and y is in megabits per second (Mbps). Based on this model, what was cable TV’s top Internet speed in 2018 to the nearest Mbps? (Data from National Cable & Telecommunications Association.) 52. Carbon Monoxide Exposure High concentrations of carbon monoxide (CO) can cause coma and death. The time required for a person to reach a carboxyhemoglobin (COHb) level capable of causing a coma can be approximated by the quadratic model T = 0.0002x2 - 0.316x + 127.9, where T is the exposure time in hours necessary to reach this level and 500 … x … 800 is the amount of carbon monoxide present in the air, in parts per million (ppm). (Data from Indoor Air Quality Environmental Information Handbook: Combustion Sources.) (a) What is the exposure time when x = 600 ppm? (b) Find the concentration of CO necessary to produce a coma in 4 hr. Round to the nearest tenth part per million. 53. Greenhouse Gas Emissions The table gives net greenhouse gas emissions from human activities in the United States, in millions of metric tons. The quadratic model y = -58.73x2 + 235.7x + 5783 approximates the net emissions for these years. In the model, x represents the number of years since 2012, so x = 0 represents 2012, x = 1 represents 2013, and so on. Year Millions of Metric Tons of Greenhouse Gas 2012 5775.3 2013 5973.3 2014 6022.8 2015 5942.9 2016 5794.5 Data from U.S. Environmental Protection Agency.
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