Textbook Problem

Obesity 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.

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

Source: American Journal of Preventive Medicine 42 (June 2012): 563-570. ajpmonline.org

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

$S(x)=\frac{0.264x^2+10.7x-66.9}{-0.00850x^2+1.25x+0.854}$

where x is the number of years after 1980. Use this function in Problems 71 and 72.

(a) Find $\underset{x\to 40}{\lim }S(x)$, if it exists.

(b) What does this limit estimate?

(c) Is the function accurate as $x\to 40$? Explain.