The body mass index (BMI) is used to identify, evaluate, and...

The body mass index (BMI) is used to identify, evaluate, and treat overweight and obese adults. The BMI value for an adult of weight $w$ (in kilograms) and height $h$ (in meters) is defined to be $$ M=f(w, h)=\frac{w}{h^{2}} $$ According to federal guidelines, an adult is overweight if he or she has a BMI value greater than 25 but less than 30 and is "obese" if the value is greater than or equal to 30. a. What is the BMI of an adult who weighs in at $80 \mathrm{kg}$ and stands $1.8 \mathrm{m}$ tall? b. What is the maximum weight for an adult of height $1.8 \mathrm{m},$ who is not classified as overweight or obese?

The body mass index (BMI) is used to identify, evaluate, and treat overweight and obese adults. The BMI value for an adult of weight $w$ (in kilograms) and height $h$ (in meters) is defined to be
$$
M=f(w, h)=\frac{w}{h^{2}}
$$
According to federal guidelines, an adult is overweight if he or she has a BMI value greater than 25 but less than 30 and is "obese" if the value is greater than or equal to 30.
a. What is the BMI of an adult who weighs in at $80 \mathrm{kg}$ and stands $1.8 \mathrm{m}$ tall?
b. What is the maximum weight for an adult of height $1.8 \mathrm{m},$ who is not classified
as overweight or obese?

Key Concepts

Solving Inequalities in a Mathematical Context

Dealing with weight classification often involves solving inequalities to determine the range of acceptable values for weight or BMI. This process requires algebraic manipulation of the BMI formula to isolate one variable, enabling a clear understanding of the limits set by established thresholds for health conditions.

Thresholds for Classification

In health assessments, specific numerical thresholds are used to categorize individuals based on their BMI values. These thresholds delineate the ranges for various categories (for example, normal weight, overweight, and obesity) and form the basis for medical guidelines, helping to standardize decisions regarding interventions and treatments.

Body Mass Index (BMI)

BMI is a quantitative measure that relates an individual’s weight to their height. It serves as a simple and quick screening tool used by health professionals to categorize individuals into various weight status groups such as underweight, normal weight, overweight, and obese. This classification helps in evaluating health risks associated with being overweight or obese.

Mathematical Function Evaluation

The BMI is calculated using a mathematical function where weight and height are input into a formula, typically defined as BMI = weight divided by the square of height. Evaluating this function involves substituting the measured values into the formula and carrying out arithmetic operations to obtain a numerical result.

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