Obesity (BMI ( 30) is a serious problem in the United States and is expected to get worse. Being overweight increases the risk of diabetes, heart disease, and many other ailments, but the severely obese (BMI ( 40) are most at risk and the most expensive to treat. The percent of Americans who are obese and severely obese from 1990 and projected to 2030 are shown in the table below.

(a) Find the linear function, O(x), that models obesity, with x equal to the number of years past 1980 and y the percent of obese Americans. Report the model as y = O(x) with 3 significant digit coefficients.

(b) Find the linear function, S(x), that models severe obesity, with x equal to the number of years past 1980 and y the percent of severely obese Americans. Report the model as y = S(x) with 3 significant digit coefficients.

(c) Let F(x) = S(x) / O(x), What is the mathematical name for this type of function, and what does it measure in terms of these data?

(d) Find the horizontal asymptote for F(x), and tell what it means in terms of these data.

Year 1990 2000 2010 2015 2020 2025 2030 12.7 22.1 30.9 34.5 37.4 39.9 42.2 4.9 % Obese % Severely Obese 7.9 9.5 11.1 2.2 6.4 0.8