198 CHAPTER 1 Equations and Inequalities Answer the following. 105. Why can 3 not be in the solution set of 14x + 9 x - 3 60? (Do not solve the inequality.) 106. Why must -4 be in the solution set of x + 4 2x + 1 Ú 0? (Do not solve the inequality.) (Modeling) Solve each problem. 101. Ozone Concentration Guideline levels for indoor ozone are less than 50 parts per billion (ppb). In a scientific study, a Purafil air filter was used to reduce an initial ozone concentration of 140 ppb. The filter removed 43% of the ozone. (Data from Parmar and Grosjean, Removal of Air Pollutants from Museum Display Cases, Getty Conservation Institute, Marina del Rey, CA.) (a) What is the ozone concentration after the Purafil air filter is used? (b) What is the maximum initial concentration of ozone that this filter will reduce to an acceptable level? Round the answer to the nearest tenth part per billion. 102. Break-Even Interval A company produces earbuds. The revenue from the sale of x units of these earbuds is R = 8x. The cost to produce x units of earbuds is C = 3x + 1500. In what interval will the company at least break even? 103. Height of a Projectile A projectile is launched upward from the ground. Its height s in feet above the ground after t seconds is given by the following equation. s = -16t2 + 320t (a) After how many seconds in the air will the projectile hit the ground? (b) During what time interval is the projectile more than 576 ft above the ground? 104. Social Security The total amount paid by the U.S. government to individuals for Social Security retirement and disability insurance benefits during the period 2008–2017 can be approximated by the linear model y = 35.6x + 626, where x = 0 corresponds to 2008, x = 1 corresponds to 2009, and so on. The variable y is in billions of dollars. Based on this model, during what year did the amount paid by the government first exceed $850 billion? Round the answer to the nearest year. Compare the answer to the bar graph. 0 200 400 600 800 1000 Billions of dollars Social Security Retirement and Disability Insurance Benefits Year ’08 ’09 ’10 ’11 ’12 ’13 ’17 ’14 ’15 ’16 Data from U.S. Office of Management and Budget.
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