As you complete more years of education, you can count on a greater income. The bar graph shows the median, or middlemost, annual income for Americans, by level of education, for a recent year.

Here are polynomial models that describe the median annual income for men, M, and for women, W, who have completed x years of education:

 M = 177x2 + 288x + 7075

 W = 255x2 − 2956x + 24,336

 M = −18x3 + 923x2 − 9603x + 48,446

 W = 17x3 − 450x2 + 6392x − 14,764.

Exercise are based on these models and the data displayed by the graph.

a. Use the equations defined by polynomials of degree 3 to find a mathematical model for M − W.

b. According to the model in part (a), what is the difference in the median annual income between men and women with 14 years of education?

c. According to the data displayed by the graph, what is the actual difference in the median annual income between men and women with 14 years of education? Did the model in part (b) underestimate or overestimate this difference? By how much?

Transcribed Image Text:

Median Annual Income, by Level of Education Men Women $90 $80 S70 S60 $50 $40 $30 $20 $10 10 12 13 14 16 18 20 Years of School Completed Median Annual Income (thou san ds of dollars) 17023 699 IZ Liz'se 691'61 35,725 26,029 41,895 30816 44,404 ist $7220 41,681 51,316 DESIZ 68875 Median Annual Income, by Level of Education Men Women $90 $80 S70 S60 $50 $40 $30 $20 $10 10 12 13 14 16 18 20 Years of School Completed Median Annual Income (thou san ds of dollars) 17023 699 IZ Liz'se 691'61 35,725 26,029 41,895 30816 44,404 ist $7220 41,681 51,316 DESIZ 68875

Answer rating: 100% (QA)

Step 1 of 7 A Below is a chart showing median annual income for group M versus group W by ... View the full answer