Problem 85 - Algebra and Trigonometry

Question

The horizontal axis shows a person's age. The vertical axis shows that person's body-mass index \((B M I),\) computed using the following formula: \(\mathrm{BMI}=\frac{703 W}{H^{2}}\) The variable \(W\) represents weight, in pounds. The variable H represents height, in inches Use this information to solve. Exercises \(85-86\) A man is 20 years old, 72 inches \((6 \text { feet })\) tall, and weighs 200 pounds a. Compute the man's BML. Round to the nearest tenth. b. Use the man's age and his BMI to locate this information as a point in the coordinate system for males. Is this person obese, overweight, borderline overweight, normal weight, or underweight?

Step-by-Step Solution

Answer

a. The man's BMI is 27.1. b. In the coordinate system, this information is represented as the point (20, 27.1). This man is considered overweight based on his BMI.

Step 1: Calculate the BMI

Use the given formula for calculating BMI: \(BMI=\frac{703W}{H^{2}}\). The weight \(W\) is given as 200 pounds and the height \(H\) is 72 inches. So substitute these values into the equation to get \(BMI=\frac{703*200}{72^{2}}\).

Step 2: Compute the BMI

Solve the above expression to compute the BMI value. It should be rounded off to the nearest tenth. Which results in BMI being approximately 27.1.

Step 3: Interpreting the BMI

Based on the computed BMI and the man's age, we determine his weight status. The universally accepted interpretation of BMI values is as follows: BMI < 18.5 is underweight, 18.5 ≤ BMI < 25 is normal weight, 25 ≤ BMI < 30 is overweight, and BMI ≥ 30 is obese. Hence, with a BMI of 27.1, the man is considered overweight.

Step 4: Locate information in the coordinate system

In the coordinate system where the horizontal axis is the person's age and the vertical axis is the person's BMI, this information can be represented as the point (20, 27.1)

Key Concepts

Coordinate System

In the context of BMI analysis, a coordinate system can be used to visually represent the relationship between age and BMI. The horizontal axis, or x-axis, typically represents the age of the individual. The vertical axis, or y-axis, represents the individual's BMI. By plotting these values, one can see where an individual stands in terms of weight status, compared to normative data. For example, in the exercise, the man’s age is 20, and his BMI is 27.1. This is plotted as a point on the coordinate system: (20, 27.1). This visual representation helps in quickly assessing weight status categories based on BMI across different ages.

Age and BMI Relationship

As people age, their Body Mass Index (BMI) can change due to various factors such as lifestyle, metabolism, and changes in body composition. It's essential to understand that BMI is only one measure of health, and age can be a factor that influences weight standards. For instance, BMI might tend to increase with age due to a decrease in muscle mass and an increase in body fat. Although BMI gives a general indication of health, it doesn't differentiate between fat and muscle. Thus, observing the trend of BMI across different ages can help in understanding how average measures deviate over time and emphasizing the importance of considering age in evaluations.

Weight Status Classification

Understanding weight status through BMI classifications helps in evaluating health risks. BMI values are divided into different categories:

• Underweight: BMI < 18.5
• Normal weight: 18.5 ≤ BMI < 25
• Overweight: 25 ≤ BMI < 30
• Obese: BMI ≥ 30

These categories indicate potential health issues. For instance, being underweight might signal nutritional deficiencies, while being overweight or obese can increase the risk of chronic conditions like diabetes or heart disease. In the exercise, the man's BMI is calculated as 27.1, which places him in the overweight category. Recognizing these classifications is crucial for taking steps toward maintaining a healthy lifestyle.

BMI Calculation Formula

The Body Mass Index (BMI) is calculated using a straightforward formula that incorporates an individual's weight and height. The formula is: \[ BMI = \frac{703 \times \text{weight in pounds}}{\text{height in inches}^2} \] In this formula, "703" is a conversion factor used to balance the units of weight (pounds) and height (inches), making the index applicable for body weight comparison regardless of height. To find BMI, you multiply the individual's weight by 703, and then divide by the square of their height in inches. It's a quick way to assess whether someone has a healthy weight for their height. However, while easy to use, remember that BMI does not consider factors like muscle mass, bone density, and overall body composition.