Chapter 6.2, Problem 66E

AVERAGE Birth Height of BOYS Using data collected at Kaiser Hospital, pediatricians estimate that the average height of male children changes at the rate of

$\text{h}\prime (\text{t})=\frac{52.8706{\text{e}}^{-0.3277\text{t}}}{{(1+2.449{\text{e}}^{-0.3277\text{t}})}^2}$

inches/year, where the child’s height h(t) is measured in inches and t, the child’s age, is measured in years, with t = 0 corresponding to birth. Find an expression h(t) for the average height of a boy at age t if the height at birth of an average child is 19.4 in. What is the height of an average 8-year-old boy?