Body Mass Index

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MATH133 Unit 3: Radicals and Rational Exponents

Discussion Board Assignment: Version 2A

Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols.

Body Mass Index

The United States is becoming more health-conscious, and as a result, the problem of obesity has

gotten more attention. The body mass index (BMI) relates a person’s height and weight, and it is

often used to determine if someone is overweight. The following table tells the weight status for

a given BMI.

BMI Weight Status

Below 18.5 Underweight

18.5–24.9 Normal

24.9–29.9 Overweight

29.9 and above Obese

The BMI is calculated using the following formula:

BMI = 703 × 𝑤

ℎ2

where w is the weight in pounds and h is the height in inches.

Solving this formula for h, we see that h = sqrt[703w / BMI] or �ℎ = �703𝑤 BMI

�

1. Using the Internet, AIU’s library, or another research source, find the weight of your

favorite celebrity. This could be a movie or television personality, athlete, or a politician.

You may also use yourself.

2. Using the weight you found in Question 1, determine the height the celebrity (or yourself)

would need to be to fall into each of the four weight status categories listed in the table.

In other words, select a BMI less than 18.5 (any value), and find h. Then, repeat using a

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new BMI in each range. Show all of your work for each of these calculations.

Chosen BMI Value Calculated Height (in.)

Underweight

Normal

Overweight

Obese

3. Using your chosen BMI values and the corresponding four heights calculated in Question

2, and using Excel or another graphing utility, draw the graph of your celebrity’s heights

as a function of the BMI. (The function being graphed is h = sqrt(703 × w / BMI), so BMI

is the independent [or horizontal] variable.) Insert the graph into a Word document, and

attach that Word document to the DB thread, or paste your graph into the DB thread.

4. Using the Internet or other library resource, find the actual height of your celebrity.

5. Using the height found in Question 4, calculate the person’s actual weight status

(underweight, normal, overweight, or obese) using the original BMI formula above.

6. What would be the height range (minimum and maximum heights) for your celebrity to

be in the normal weight status? In other words, based on your celebrity’s weight, what

would be the heights of the celebrity at BMIs of 18.5 and 24.9? (Show these

calculations.)

7. Based on the celebrity’s appearance, would you consider him or her to actually be in the

weight status that this formula says based on his or her actual height and weight and

considering his or her other physical characteristics? Why or why not? Think about why

there may be differences in your calculations and the actual figures.

8. The BMI formula was created by a Belgian statistician (not a physician), Lambert

Adolphe Quetelet, in about 1832. Quetelet was trying to determine the “average” person’s

weight relative to his or her height. His “Quetelet index” (later known as the BMI) was

developed using height and weight data of Europeans in the early 1800s. Do you think

that BMI is a fair indication of a person’s weight classification today? Why or why not?

9. According to data collected by the Centers for Disease Control (CDC) National Health

and Nutrition Examination Survey III, the following quadratic functions approximately

represent the median BMI values for men and women in the United States, where x is

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their age (Halls, 2008; Halls, 2008):

Men: BMI = −0.0031𝑥2 + 0.3256𝑥 + 20.2085

Women: BMI = −0.0036𝑥2 + 0.3754𝑥 + 19.4353

10. For your celebrity’s age, calculate the median BMI from the appropriate quadratic

function above. Is your celebrity’s actual BMI over or under this calculated median

value? (Show all of your work.)

11. After studying BMI, why do you think that BMI is so widely used by the federal

government, health industry professionals, and insurance companies as a measure of a

person’s overall health?

12. Summarize your findings in writing using proper style and grammar.

13. Which intellipath Learning Nodes helped you with this assignment?

References

Formatting math as text. (n.d.). Retrieved from the Purple Math Web site:

http://www.purplemath.com/modules/mathtext.htm

Halls, S. B. (2008). Body mass index charts of men. Retrieved from http://www.halls.md/body-

mass-index/mens.htm

Halls, S. B. (2008). Body mass index charts of women. Retrieved from

http://www.halls.md/body-mass-index/womens.htm