A male child is 19 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. (Round b to two decimal places.) (b) Suppose he reaches 91% of his adult height at age 16. Use this information and that from part (a) to find r. (Suggestion: Vou will need to use either the crossing-graphs method or some algebra involving the logarithm. Round r to three decimal places.) (e) Make a logistic model for the height H, in inches, as a function of the age r, in years. H(t) = (d) According to the logistic model, at what age is he growing the fastest? (Round your answer to two decimal places.) years old

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A male child is 19 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. (Round b to two decimal places.)
K=
b =
(b) Suppose he reaches 91% 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. Round r to three decimal places.)
(c) Make a logistic model for the height H, in inches, as a function of the age t, in years.
H(t) =
C) According to the logistic model, at what age is he growing the fastest? (Round your answer to two decimal places.)
years old
Transcribed Image Text:A male child is 19 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. (Round b to two decimal places.) K= b = (b) Suppose he reaches 91% 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. Round r to three decimal places.) (c) Make a logistic model for the height H, in inches, as a function of the age t, in years. H(t) = C) According to the logistic model, at what age is he growing the fastest? (Round your answer to two decimal places.) years old
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