Question

W A person's Body Mass Index is I = H2 where W is the body weight (in kilograms) and H is the body height (in meters). Estimate the change in height that will decrease I by 1 if (W, H) = (31, 1.2), assuming that W remains constant. (Use decimal notation. Give your answer to three decimal places.) AH~

Answer 1

To estimate the change in height that will decrease the Body Mass Index (BMI) by 1, we can use the given formula and solve for ΔH. The change in height is approximately 1.320 meters.

Step-by-step explanation:

To estimate the change in height that will decrease the Body Mass Index (BMI) by 1, we can use the formula I = W/H^2, where I is the BMI, W is the body weight in kilograms, and H is the body height in meters. We are given that (W, H) = (31, 1.2) and we need to find the change in height (ΔH) that decreases the BMI by 1, while keeping the weight constant.

We can set up the equation like this:

1 = 31 / (1.2 + ΔH)^2

To solve for ΔH, we can rearrange the equation:

(1.2 + ΔH)^2 = 31

ΔH^2 + 2.4ΔH + 1.44 = 31

ΔH^2 + 2.4ΔH - 29.56 = 0

Using the quadratic formula, we can find the solutions for ΔH:

ΔH = (-2.4 ± √(2.4^2 - 4 * 1 * (-29.56))) / (2 * 1)

Using a calculator, we find that ΔH ≈ -4.320 or ΔH ≈ 1.320.

Since negative height does not make sense in this context, we can conclude that the change in height that will decrease the BMI by 1, while keeping the weight constant, is approximately 1.320 meters.