Inequalities Read The Following Instructions In Order To Com

Inequalitiesread The Following Instructions In Order To Complete This

Read the article about Body Mass Index (BMI) on page 151 of Elementary and Intermediate Algebra. Use the formula given using pounds and inches for finding the BMI at the end of the first paragraph in order to find the four intervals the article mentions: 17 30 obese. You will use your height to plug into the formula to solve for W, the weight range that will go with each category. You may prefer to solve the formula for the variable W before plugging in values, which is fine.

Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, please make sure to include: Your solution to the above problem, making sure to include all mathematical work. A discussion on the computed weight ranges and some reasons why they could be misleading. An evaluation of the regions outside of the “probably not overweight” range using both set notation and interval notation. Include a simple graph of the regions. (See Instructor Guidance example for some ideas of how to do this.) The incorporation of the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing: Inequality, Equivalent, Compound inequality, Interval, Infinity. Do not write definitions for the words; but integrate them into your discussion.

Paper For Above instruction

Body Mass Index (BMI) is a widely used metric to categorize individuals based on their weight relative to height, aiding in health assessments and predicting health risks. The formula to calculate BMI in imperial units (pounds and inches) is:

\(\text{BMI} = \frac{703 \times W}{H^2}\)

where \(W\) is weight in pounds, and \(H\) is height in inches. Using this formula, we aim to find the weight ranges corresponding to the BMI intervals specified in the article, namely: 17 30, for a given height.

Suppose an individual’s height is 65 inches (5 feet 5 inches). First, we solve the formula for \(W\):

\(\text{BMI} = \frac{703 \times W}{H^2}\)

Rearranged to solve for \(W\), it becomes:

\(W = \frac{\text{BMI} \times H^2}{703}\)

Plugging in \(H = 65\) inches gives:

\(W = \frac{\text{BMI} \times 4225}{703}\)

Now, for each interval, substitute the bounds of BMI to find the corresponding weight ranges:

- For 17

\(W_{lower} = \frac{17 \times 4225}{703} \approx 102.07\) pounds

\(W_{upper} = \frac{22 \times 4225}{703} \approx 132.50\) pounds

- For 23

\(W_{lower} = \frac{23 \times 4225}{703} \approx 138.08\) pounds

\(W_{upper} = \frac{25 \times 4225}{703} \approx 150.52\) pounds

- For 25

\(W_{lower} = \frac{25 \times 4225}{703} \approx 150.52\) pounds

\(W_{upper} = \frac{29.9 \times 4225}{703} \approx 179.83\) pounds

- For BMI > 30:

\(W_{lower} = \frac{30 \times 4225}{703} \approx 180.23\) pounds

These weight ranges illustrate the categories for someone of 65 inches in height.

However, these computed ranges could be misleading due to several factors. For instance, BMI does not account for muscle mass; a muscular individual could be classified as overweight while having low body fat. Variations in body composition, age, and ethnicity can also affect BMI's accuracy in health assessment. Furthermore, the adherence to these ranges does not guarantee health outcomes, as they serve as general guidelines rather than definitive measures.

Beyond the "probably not overweight" region (17

- Overweight region: \(\{W \;|\; W 132.50\}\) pounds, corresponding to the union of intervals outside the BMI 17–22 range.

In interval notation, the regions outside of the interval [102.07, 132.50] pounds are:

\(\left(-\infty, 102.07\right) \cup \left(132.50, \infty\right)\)

A simple graph illustrating these regions would display the weight on the x-axis with shaded areas indicating the 'healthy' BMI interval between 102.07 and 132.50 pounds, and the regions outside showing potential health risks.

In conclusion, while BMI provides a convenient tool to categorize health risk based on weight and height, it is important to understand the limitations of the inequalities involved. The concept of an interval helps visualize the acceptable weight range, while the notion of infinity underscores the unbounded nature of weights outside these ranges. Recognizing these mathematical principles enhances our interpretation of BMI's role in health assessments and the importance of comprehensive evaluations beyond simple inequalities.

References

  • Cleveland Clinic. (2020). Body Mass Index (BMI). https://my.clevelandclinic.org/health/articles/22436-bmi
  • World Health Organization. (2021). BMI classifications. https://www.who.int/news-room/fact-sheets/detail/obesity-and-overweight
  • Centers for Disease Control and Prevention. (2022). About BMI for adults. https://www.cdc.gov/healthyweight/assessing/bmi/adult_bmi/index.html
  • American Heart Association. (2019). Understanding BMI. https://www.heart.org/en/healthy-living/healthy-eating/healthy-weight/bmi-and-healthy-weights
  • Kuczmarski, R. J., et al. (2002). CDC growth charts: United States. Advance Data, (314), 1-27.

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