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Mathematics

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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.
703𝑤
Solving this formula for h, we see that h = sqrt[703w / BMI] or �ℎ = � 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:
Women:
BMI = −0.0031𝑥 2 + 0.3256𝑥 + 20.2085
BMI = −0.0036𝑥 2 + 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/bodymass-index/mens.htm
Halls, S. B. (2008). Body mass index charts of women. Retrieved from
http://www.halls.md/body-mass-index/womens.htm
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