Answer
a) \$50082; underestimate; \$494
b) $1.8x^{3}-82x^{2}+2644x-11449$
c) \$17236
d) \$18119; underestimate; \$883
Work Step by Step
a) To find the median annual income of a woman with 18 years of education, substitute $x$ with 18 in the model $316x^{2}-4224x+23730$. The answer comes to be \$50082. Looking at the graph, a women with 18 years of education made a median annual income of \$50,576. The answer from the model is less than the graph value by \$494, meaning it underestimates the actual value.
b) The model of $M-W$ with a degree of 3 is found by subtracting ($-1.2x^{3}+367x^{2}-4900x+26561$) 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 find the difference in the median annual income between men and women with 16 years of education, plug 16 into $x$ for the model found in part b. The answer comes to be \$17236.
d) Looking at the graph, the actual difference bewteen median annual incomes for men and women with 16 years of education is \$18119. This is calculated by finding the difference of \$54091-\$35972. The answer in part c is less than the answer from the graph, so it underestimated the actual answer by \$883 (\$18119-\$17236).
