Question

A person's Body Mass Index is I=W/H^2, where W is the body weight (in kilograms) and H is the body height (in meters).

A boy has weight W=62 kg and height H=1.65. Use the linear approximation to estimate the change in I if (W,H) changes to (66,1.69).
Find Dealta I=

Answer 1

To estimate the change in BMI (ΔI) when the weight changes from 62 kg to 66 kg and the height from 1.65 m to 1.69 m, calculate the initial and final BMI using the formula I = W/H^2, then find the difference. The estimated change is ΔI = 0.34.

Step-by-step explanation:

The student is asking how to estimate the change in Body Mass Index (BMI) given a change in weight and height using the linear approximation. The initial weight (W) is 62 kg and the initial height (H) is 1.65 m. The new weight is 66 kg and the new height is 1.69 m. To find the change in BMI, we can use the formula I = W/H2, and calculate the initial and final BMI.

Initial BMI: Iinitial = 62 / 1.652 = 22.77

Final BMI: Ifinal = 66 / 1.692 = 23.11

Now we calculate the change in BMI (ΔI) by subtracting the initial BMI from the final BMI:

ΔI = Ifinal - Iinitial = 23.11 - 22.77 = 0.34

Therefore, the estimated change in BMI (ΔI) is 0.34.