Chapter 5.1, Problem 20E

Modeling Human Height with a Logistic Function A male child is $21\text{inches}$ long at birth and grows to an adult height of $73\text{inches}$. In this exercise, we make a logistic model of his height as a function of age.

a. Use the given information to find $K$ and $b$ for the logistic model.

b. Suppose he reaches 95% of his adult height at age $16$. Use this information and that from part a to find $r$. (Suggestion: You will need to use either the crossing-graphs method or some algebra involving the logarithm.)

c. Make a logistic model for his height $H$, in inches, as a function of his age t, in years.

d. According to the logistic model, at what age is he growing the fastest?

e. Is your answer to part d consistent with your knowledge of how humans grow?