889 9.1 Systems of Linear Equations Changes in Population The graph shows the populations of the New Orleans, LA, and the Jacksonville, FL, metropolitan areas over the years 2004–2017. ’04 ’05 ’06 ’07 ’08 ’09 0 0.9 1.0 1.3 1.2 1.1 1.5 1.4 Year Number (in millions) Population of Metropolitan Areas Data from U.S. Census Bureau. ’10 ’11 ’12 ’13 ’14 ’15 ’16 ’17 New Orleans Jacksonville 93. In what years was the population of the Jacksonville metropolitan area greater than that of the New Orleans metropolitan area? 94. At the time when the populations of the two metropolitan areas were equal, what was the approximate population of each area? Round to the nearest hundredth million. 95. Express the solution of the system as an ordered pair to the nearest tenth of a year and the nearest hundredth million. 96. Use the terms increasing, decreasing, and constant to describe the trends for the population of the New Orleans metropolitan area. 97. If equations of the form y = ƒ1t2 were determined that modeled either of the two graphs, then the variable t would represent and the variable y would represent . 98. Why is each graph that of a function? Solve each problem. See Examples 5 and 9. 99. Unknown Numbers The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers. 100. Costs of Goats and Sheep At the Berger ranch, 6 goats and 5 sheep sell for $305, while 2 goats and 9 sheep sell for $285. Find the cost of a single goat and of a single sheep. 101. Fan Cost Index The Fan Cost Index (FCI) is a measure of how much it will cost a family of four to attend a professional sports event. In 2018, the FCI prices for Major League Baseball and the National Football League averaged $383.34. The FCI for baseball was $305.40 less than that for football. What were the FCIs for these sports? (Data from Team Marketing Report.) 102. Money Denominations A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is $351. How many of each denomination of bill are there? (a) If the quadratic relationship between C and S is written as C = aS2 + bS + c, use a system of linear equations to determine the constants a, b and c, and give the equation. (b) A new aircraft of this type has a ceiling of 45,000 ft. Predict its top speed to the nearest knot.
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