Answer
a) 2078 calories; underestimates the graph value by 22 calories
b) 2662 calories; underestimates the graph value by 38 calories
c) $\frac{-33x^{2}+263x+515}{-60x^{2}+499x+295}$
Work Step by Step
a) Plug 4 into x in the $W$ model since the age range 19 to 30 is in age group 4 on the graph. $-66(4)^{2}+526(4)+1030=2078$. This underestimates (less than) the graph value of 2100 calories by 22 calories (2100-2078=22).
b) Plug 4 into x in the $M$ model since the age range 19 to 30 is in age group 4 on the graph. $-120(4)^{2}+998(4)+590=2662$. This underestimates (less than) the graph value of 2700 calories by 38 calories (2700-2662=38).
c)The ratio will compare the model for women to that for men, so the fraction will take the form $\frac{W}{M}$. Therefore, $\frac{-66x^{2}+526x+1030}{-120x^{2}+998x+590}$ has to be simplified. Find the greatest common factor (GCF) between the terms in the numerator and denominator separately. In both, the GCF is 2. After dividing each term by 2, the model becomes $\frac{-33x^{2}+263x+515}{-60x^{2}+499x+295}$.
