Answer
a) \$54647; overestimate; \$556
b) $1.8x^{3}-82x^{2}+2644x-11449$
c) \$14434
d) \$15136; underestimate; \$702
Work Step by Step
a) Using the equation $M$$=$$312$$x^{2}$$-2615x$$+16615$, plug 16 into $x$ to determine the median annual income for a man with 16 years of education. The answer comes to be \$54647. When this is compared to the graph value of \$54091, it can be seen that the answer from the model overestimates (is larger) the answer from the graph. To determine by how much the model overestimates the median annual income, subtract \$54091 from \$54647 (model income$-$graph income) to get \$556.
b) To find $M-W$ for a degree of 3, subtract ($-1.2x^{3}+367x^{2}-4900x+26561$) from ($0.6x^{3}+285x^{2}-2256x+15112$) to get $1.8x^{3}-82x^{2}+2644x-11449$. Remember to distribute the minus sign when solving.
c) To solve the difference in income for men and women with 14 years of education using the model in part b, plug 14 into x. The difference rounded to the nearest dollar is \$14434.
d) When looking at the graph for the difference in incomes for men and women with 14 years of education, it can be seen that \$42163$-$\$27027$=$\$15136. The answer found in part c underestimates this value by \$702 (\$15136$-$\$14434).
