179 1.7 Inequalities These receipts R are reasonably approximated by the linear model R = 0.2219x + 7.200, where x = 0 corresponds to 1997, x = 5 corresponds to 2002, and so on. Using the model, calculate the year in which the receipts first exceed each amount. (a) $8.1 billion (b) $10.6 billion 88. Recovery of Solid Waste The percent W of municipal solid waste recovered through recycling and composting is shown in 5-year increments in the bar graph. The linear model W= 0.4700x + 26.16, where x = 0 represents 1995, x = 5 represents 2000, and so on, fits the data reasonably well. (a) Based on this model, when did the percent of waste recovered first exceed 32.5%? (b) During what years was the percent of waste recovered between 30% and 34%? 0 10 20 40 30 Percent Municipal Solid Waste Recovered ’95 ’00 ’05 ’10 ’15 Year Data from U.S. Environmental Protection Agency. 28.5 25.7 31.4 34.0 34.7 Solve each problem. See Example 7. 89. Height of a Projectile A projectile is fired straight up from ground level. After t seconds, its height above the ground is s feet, where s = -16t2 + 220t. For what time period is the projectile at least 624 ft above the ground? 90. Height of a Projectile See Exercise 89. For what time period is the projectile at least 744 ft above the ground? 91. Height of a Baseball A baseball is hit so that its height, s, in feet after t seconds is s = -16t2 + 44t + 4. For what time period is the ball at least 32 ft above the ground? 92. Height of a Baseball See Exercise 91. For what time period is the ball greater than 28 ft above the ground? 93. Velocity of an Object Suppose the velocity, v, of an object is given by v = 2t2 - 5t - 12, where t is time in seconds. (Here t can be positive or negative.) Find the intervals where the velocity is negative. 94. Velocity of an Object The velocity of an object, v, after t seconds is given by v = 3t2 - 18t + 24. Find the interval where the velocity is negative.
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