This essay is about BMI (body mass index). I am going to figure out, how my weight and height correlate with health state, according to the BMI index. I will use imperial BMI formula to calculate weight ranges using my height. Later I’ll use the BMI figures from the inequalities and find out the weight intervals and corresponding weight intervals.
The formula of BMI is the following:
BMI (Body Mass Index) = (Weight, pounds) * 703 / (Height, inches) ^2
I’ll start with inserting my height into this formula. It is equal to 6 ft. and I’ve got to convert it into inches. One foot is 12 inches and 6 feet will be equal to 6*12 = 72 inches.
I am going to transform the BMI formula little bit:
W = (BMI * (height in inches) ^2) / 703
Some preparations before using the formula in inequalities:
W = (BMI * 72 ^2) / 703
W = (BMI * 5184) / 703
After dividing 5184 by 703 I got 7,374, I will round it up and use just 7. The formula will look like:
W = BMI * 7
Our intervals are:
17 < BMI < 22 might have a longer life span than average 23 < BMI < 25 probably not overweight 25 < BMI < 29.9 probably overweight
BMI ≥ 30 obese
The next step would be calculation of Weight equivalents for all of BMIs, including the last compound inequality, which shows, that the person is obese, if his Body Mass Index is more than 30 and goes to infinity.
- If BMI is equal to 17, than the weight = 119, because Weight = BMI * 7
- If BMI is equal to 22, than the weight = 154, because Weight = BMI * 7
- If BMI is equal to 23, than the weight = 161, because Weight = BMI * 7
- If BMI is equal to 25, than the weight = 175, because Weight = BMI * 7
- If BMI is equal to 29.9, than the weight = 209, because Weight = BMI * 7
- If BMI is equal to 30, than the weight = 210, because Weight = BMI * 7
At this stage, I can already construct the intervals, using Weight values, set notations and show the results on the graphs:
- 119 < W < 154 might have a longer life span than average
Interval notation {W|119 < W < 154};
Set notation (119; 154);
- 161 < W < 175 probably not overweight
Interval notation {W|161 < W < 175};
Set notation (161; 175);
- 175 < W < 209 probably overweight
Interval notation {W|175 < W < 209};
Set notation (175; 209);
- W ≥ 210 obese
Interval notation {W| W ≥ 210};
Set notation [210 ;+∞);
Now I will evaluate the regions outside of the “probably not overweight”.
Inequalities for these regions are:
119 < W < 154
210 > W
Interval notation {W| 119
Set notation (119 ;154) U (210; ∞);
I computed all the weight ranges, but there are at least two reasons why the BMI index can be misleading. The first reason is that the BMI index does not differentiate, the weight consists of fat or muscles. Some people can have more fat and the others can have more muscles and heavier bones but their BMI can be the same. The second problem is that in our inequalities we have no definition for the range of weights [154; 161].
References:
- Inequalities. (n.d.). Math.com – The World of Math Online Retrieved from http://www.math.com/school/subject2/lessons/S2U3L4GL.html
Set notation (119 ;154) U (210; ∞);
I computed all the weight ranges, but there are at least two reasons why the BMI index can be misleading. The first reason is that the BMI index does not differentiate, the weight consists of fat or muscles. Some people can have more fat and the others can have more muscles and heavier bones but their BMI can be the same. The second problem is that in our inequalities we have no definition for the range of weights [154; 161].
References:
- Inequalities. (n.d.). Math.com – The World of Math Online Retrieved from http://www.math.com/school/subject2/lessons/S2U3L4GL.html
