Question

Sam was 28 inches tall on her first birthday, 50 inches tall on her 8th, and 62 inches tall on her 14th.

a) Let t represent Sam's age in years, and let h represent her height in inches. Determine the values of M,A, and k for a logistic model, h(t)=(M/ 1+Ae^-kt), that fits the given height data.

b) What is Sam's theoretical long-term expected height? That is, what is lim t->infinity h(t) ?

c) At what age does the model predict that Sam will reach 95% of her expected maximum height?

Answer 1