As you (.:omplete more years of education, you c.an comll 011 a greater in.L~ome. Tlze

Chapter 0, Problem 91

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As you (.:omplete more years of education, you c.an comll 011 a greater in.L~ome. Tlze bar graph shows lhe median, or middlemost, awwal income for Americ-ans, by level of education, in 2009. 590 580 S70 s~ S50 540 530 520 SIO Median Annual Income, by leel of Education, 2009 Men Women 12 13 14 16 18 20 Years of School Completed Source: Bureau of the Census Here are polynomial mode/J that describe the median annual income for men, M, and for women, tV, who have completed x ye-ars of education:M - 312t1 - 261 5x + 16.615IV - 316x2 - 4224x + 23,730M - 0.6x3 + 285x2 - 2256x + 15,112IV - - 1.2t3 + 367x1 - 4900x ~ 26,561Exercises 9/-92 are based on these models and the data displayed by the graph at the boftom of the pre"ious page. a. Use the equation defined by a polynomial of degree 2 to find the median annual income for a man with 16 years of education. Does this underestimate or overestimate the median income shown by the bar graph? By how much'! b. Use the equations defined by polynomials of degree 3 to find a mathematical model forM - W. r. According to the model in part (b), what is the difference, rounded to the nearest dollar, in the median annual income between men and women with 14 years of education? d. According to the data displayed by the graph, what is the actual difference in the median annual income be tween men and women with 14 years of education? Did the result of part (c) underestimate o r overestimate this difference? By how much?