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 following table shows the percent of obese Americans who are severely obese for selected years from 1990 and projected to 2030.

The percent of obese American adults who are severely obese can be modeled by the function

where x is the number of years after 1980. Use this function in Problem.

(a) Find lim_x→40 S(x), if it exists.
(b) What does this limit estimate?
(c) Is the function accurate as x → 40? Explain.

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Percent Obese Who Are Severely Obese Year 1990 2000 2010 2015 2020 2025 2030 Percent 6.30 9.95 15.9 18.6 21.1 23.8 26.3