The guidelines for a healthy adult are to maintain a Body Ma

The guidelines for a healthy adult are to maintain a Body Mass Index (BMI) between 19.5 and 24.9. A formula that relates the height of an adult to his or her weight and BMI is h = 40 squareroot 0.45 W/M, where h = height in inches, w = weight in pounds, and M = BMI. Suppose Lauren is 5\'4\" and has a BMI of 18.5. How many whole pounds must she gain or lose to be within the healthy BMI range? Who has a wider weight range for a healthy BMI, a shorter person or a taller person? Use algebra and logic to justify your answer.

Solution

16) H = 40sqrt[0.45w/M]

= 40sqrt[0.45*w/18.5]

H = 5\'4\" = 64inches

So, 64 = 40sqrt[(0.45*w/18.5]

64/40 = sqrt[(0.45*w/18.5]

quaring both sides: w =105.58 lb

17) H = 40sqrt[0.45w/M]

H^2 = 1600[0.45w/M]

M = 1600*0.45*w/H^2

M is inversely proprtional to square of height. So, man with a taller height would have smaller BMI

and can have wider range of BMI avaiable.However, shorter man would have a larger BMI and narrow rangewith the standrad range of BMI.