Obesity (BMI ‰¥ 30) is a serious problem in the United States and 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 are the most expensive to treat. The percent of
Americans who are obese and severely obese from 1990 projected to 2030 are shown in the table below. Report the following models with three significant digits.
(a) Find the linear function, O(x), that models the percent of Americans who are obese, with x equal to the number of years past 1980.
(b) Find the linear function, S(x), that models the percent of Americans who are severely obese, with x equal to the number of years past 1980.
(c) Form the rational function F(x) that gives the fraction of obese Americans who are severely
obese.

(e) What does part (d) tell us about the graph of y=F(x)?
(f) Does F(x) have any vertical asymptotes for x > 0?

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