Section 1.3 The Order of Operations, Algebraic Expressions, and Equations 35 6c. The number of viewers (in millions) for the season premiere of Fox Network’s American Idol for Seasons 1 to 8 is shown in the table. i. The number of viewers can be approximated by the expression 0.1x3 + 18.4x - 2.54x2 - 4.6, where x is the number of seasons aired. Write an equation that represents the approximate number of viewers, where v is the number of viewers in millions. ii. Use the equation to estimate the number of viewers for Season 9 (Jan. 2010). Solution 6c. i. The equation that represents the number of viewers, in millions, is v = 0.1x3 + 18.4x - 2.54x2 - 4.6. ii. v = 0.1x3 + 18.4x - 2.54x2 - 4.6 v = 0.1(9)3 + 18.4(9) - 2.54(9)2 - 4.6 Replace the variable x with 9. v = 0.1(729) + 18.4(9) - 2.54(81) - 4.6 Evaluate the exponential expressions. v = 72.9 + 165.6 - 205.74 - 4.6 Add or subtract from left to right. v = 28.16 The expression estimates that there were approximately 28.16 million, or 28,160,000, viewers for Season 9. 6d. The basal metabolic rate (BMR) is the number of calories a person burns to sustain life. It is the number of calories burned even if a person stayed in bed all day. It is based on a person’s height, weight, and age. The BMR for women is 655 plus 4.35 times a person’s weight in pounds plus 4.7 times a person’s height in inches minus 4.7 times a person’s age. i. Write an equation that represents a woman’s BMR, where w is the woman’s weight (in pounds), h is the woman’s height (in inches), and a is the woman’s age. ii. If Susan is a 35-yr-old who weighs 145 lb and is 5 ft 2 in. tall, what is her BMR? Round to the nearest integer. Solution 6d. i. The equation that represents a woman’s basal metabolic rate is given by BMR is 655 plus 4.35 times weight plus 4.7 times height minus 4.7 times age BMR = 655 + 4.35w + 4.7h - 4.7a ii. To find Susan’s BMR, we must make appropriate substitutions for the variables. We are given that w = 145, h = 62, and a = 35. So, her BMR is BMR = 655 + 4.35w + 4.7h - 4.7a BMR = 655 + 4.35(145) + 4.7(62) - 4.7(35) BMR = 655 + 630.75 + 291.4 - 164.5 BMR = 1412.65 Susan’s BMR is approximately 1413 calories. Season Viewers (in millions) 1 (2002) 9.9 2 (2003) 26.5 3 (2004) 28.56 4 (2005) 33.58 5 (2006) 35.53 6 (2007) 37.7 7 (2008) 33.4 8 (2009) 30.4
hendricks_beginning_algebra_1e_ch1_3
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