   Chapter 9.1, Problem 69E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
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.orgThe percent of obese American adults who are severely obese can be modeled by the function S ( x ) = 0.264 x 2 + 10.7 x − 66.9 − 0.00850 x 2 + 1.25 x + 0.854 where x is the number of years after 1980. Use this function in Problems 71 and 72.(a) Find lim x → 60 S ( x ) , if it exists.(b) What does this limit predict?(c) Does this prediction seem plausible? Explain.

(a)

To determine

To calculate: The value of limx60S(x), if it exists.

Explanation

Given Information:

The provided 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

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

S(x)=0.264x2+10.7x66.90.00850x2+1.25x+0.854

Where x is the number of years after 1980.

Formula used:

For a polynomial function f(x)=anxn+an1xn1++a1x+a0 where an0 and n is a positive integer,

limxcf(x)=f(c)

This is defined for all values of c.

Calculation:

Consider the provided function,

S(x)=0.264x2+10.7x66.90.00850x2+1.25x+0.854

Substitute it in the limit limx60S(x),

limx60S(x)=limx60(0

(b)

To determine

The prediction made by the limit limx60S(x).

(c)

To determine

Whether the prediction made by the limit limx60S(x) is plausible.

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