Modeling human height with a logistic function: A male child is 21 inches long at birth and grows to an adult height of 73 inches. In this exercise we make a logistic model of his height as a function...

Modeling human height with a logistic function: A male child is 21 inches long at birth and grows to an adult height of 73 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 the height H, in inches, as a function of the 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?