Recall from Exercise 47, Section 7.1, that the surface area of a person’s body may be estimated by the empirical formula S(W, H) = 0.0072W^0.425H^0.725 where W is the person’s weight in kilograms, H is the person’s height in centimeters, and the surface area S is measured in square meters.

a. Find the average value of the function S(W, H) over the region R: 3.2 ≤ W ≤ 80, 38 ≤ H ≤ 180

b. A child weighs 3.2 kg and is 38 cm tall at birth and as an adult, has a stable weight of 80 kg and height of 180 cm. Can the average value in part (a) be interpreted as the average lifetime surface area of this person’s body? Explain.

Data from Exercise 47, Section 7.1

Pediatricians and medical researchers sometimes use the following empirical formula* relating the surface area S (m²) of a person to the person’s weight W (kg) and height H (cm):

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S(W, H)= 0.0072 W0.425H0.725