Chapter P.4, Problem 92PE

(a)

To determine

To calculate: The annual income for a woman with 18 years of education by using degree 2 polynomial and then calculate by how much the median annual income underestimate or overestimate if the bar graph shown below represents the median annual income for Americans by level of education in 2009 and the polynomials models that described the median annual income for men M, for women W who have completed x years of education are,

$\begin{array}{c}M=312x^2-2615x+16,615\\ W=316x^2-4224x+23,730\\ M=0.6x^3+285x^2-2256x+15,112\\ W=-1.2x^3+367x^2-4900x+26,561\end{array}$

And the bar graph is,

(b)

To determine

To calculate: The mathematical model for $M-W$ by using degree 3 polynomial model if the bar graph represents the median annual income for Americans by level of education in 2009 and the polynomials models that described the median annual income for men M, for women W who have completed x years of education are,

$\begin{array}{c}M=312x^2-2615x+16,615\\ W=316x^2-4224x+23,730\\ M=0.6x^3+285x^2-2256x+15,112\\ W=-1.2x^3+367x^2-4900x+26,561\end{array}$

(c)

To determine

To calculate: The median annual income between men and women with 16 years of education by using part (b) mathematical model $1.8x^3-82x^2+2644x-11449$.

(d)

To determine

To calculate: The actual difference in the median annual income between men and women with 16 years of education by using the graph and then calculate by how much the median annual income underestimate or overestimate by the part (c) result of $\$17,235$ if the bar graph shown below represents the median annual income for Americans by level of education in 2009 as,

That is,