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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 9.1, Problem 70E
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Mathematical Applications for the ...

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

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 3CP
Problem 4CP
Problem 5CP
Problem 6CP
Problem 7CP
Problem 8CP
Problem 9CP
Problem 10CP
Problem 2E
Problem 1E
Problem 4E
Problem 3E
Problem 6E
Problem 5E
Problem 8E
Problem 7E
Problem 10E
Problem 9E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 16E
Problem 15E
Problem 18E
Problem 17E
Problem 20E
Problem 19E
Problem 22E
Problem 21E
Problem 24E
Problem 23E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
BuyFindarrow_forward

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.org

The 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 → 40 S ( x ) , if it exists.

(b) What does this limit estimate?

(c) Is the function accurate as x → 40 ? Explain.

(a)

To determine

To calculate: The value of limx→40S(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+10.7x−66.9−0.00850x2+1.25x+0.854

Where x is the number of years after 1980.

Formula used:

For a polynomial function f(x)=anxn+an−1xn−1+⋯+a1x+a0 where an≠0 and n is a positive integer,

limx→cf(x)=f(c)

This is defined for all values of c.

Calculation:

Consider the provided function,

S(x)=0.264x2+10.7x−66.9−0.00850x2+1.25x+0.854

Substitute it in the limit limx→40S(x),

limx→40S(x)=limx→40(0

(b)

To determine

The estimation made by the limit limx→40S(x).

(c)

To determine

Whether the function is accurate as x approaches 40.

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Sect-9.1 P-1CPSect-9.1 P-2CPSect-9.1 P-3CPSect-9.1 P-4CPSect-9.1 P-5CPSect-9.1 P-6CPSect-9.1 P-7CPSect-9.1 P-8CPSect-9.1 P-9CPSect-9.1 P-10CP
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