As you complete more years of education, you can count on a greater income. The bar graph...

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, in 2009.

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

Exercise are based on these models and the data displayed by the graph at the bottom of the previous page.

a. Use the equation defined by a polynomial of degree 2 to find the median annual income for a woman with 18 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 for M – W

---

c. 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 16 years of education?

---

d. According to the data displayed by the graph, what is the actual difference in the median annual income between men and women with 16 years of education? Did the result of part (c) underestimate or overestimate this difference? By how much?