Question

A person's Body Mass Index is =WH2, where W is the body weight (in kilograms) and H is the body height (in meters). Estimate the change in height that will decrease by 1 if (W,H)=(29,1.3), assuming that W remains constant. (Use decimal notation. Give your answer to three decimal places.)

Answer 1

To estimate the change in height that will decrease a person's Body Mass Index (BMI) by 1, we can find the derivative of the BMI function with respect to height (H) and substitute the given values. The estimated change in height is approximately 25.47 meters.

Step-by-step explanation:

To estimate the change in height that will decrease a person's Body Mass Index (BMI) by 1, we need to find the derivative of the BMI function with respect to height (H). The derivative is given by d(BMI)/dH = -2WH⁻³. We can then substitute the values of W and H from the given information (W=29kg, H=1.3m) into the derivative equation to find the rate of change of the BMI with respect to height. Multiplying this rate by -1 will give us the estimated change in height that will decrease the BMI by 1.

Using the given information, the derivative of the BMI function is d(BMI)/dH = -2(29)(1.3)⁻³ = -25.47.

Multiplying this by -1, we get an estimated change in height of 25.47 meters, rounded to 3 decimal places. Therefore, a decrease in height of approximately 25.47 meters will decrease the BMI by 1, assuming the weight (W) remains constant.