Question

A person's Body Mass Index is =WH2,I=WH2, where WW is the body weight (in kilograms) and HH is the body height (in meters). A child has weight W=39 kgW=39 kg and height H=1.4 m.H=1.4 m. Use the linear approximation to estimate the change in I if (W,H)(W,H) changes to (41,1.43).(41,1.43).

(Use decimal notation. Give your answer to three decimal places.)

Answer 1

To estimate the change in the Body Mass Index (BMI), we can use the linear approximation. Given the initial weight and height of a child, and the new weight and height, we can calculate the change in BMI. The estimated change in BMI is 0.155.

Step-by-step explanation:

To estimate the change in the Body Mass Index (BMI), we can use the linear approximation. The formula for BMI is I = W/H^2, where W represents the body weight in kilograms and H represents the body height in meters. Given that the initial weight and height are W = 39 kg and H = 1.4 m, and the new weight and height are W = 41 kg and H = 1.43 m, we need to calculate the change in I.

Step 1: Calculate the initial BMI using the formula I = W/H^2. Substitute the initial values into the formula: I = 39/(1.4^2) = 39/1.96 = 19.898.

Step 2: Calculate the new BMI using the formula I = W/H^2. Substitute the new values into the formula: I = 41/(1.43^2) = 41/2.0449 = 20.053.

Step 3: Calculate the change in BMI by subtracting the initial BMI from the new BMI: Change in I = 20.053 - 19.898 = 0.155.

Therefore, the estimated change in the Body Mass Index (BMI) is 0.155.