A child is 22 inches long at birth and grows to an adult height of 70 inches.

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A: Make a logistic model of the height  H, in inches, at age  t years. Note:  Thus far you are not given sufficient information to determine the value of r in the expression .  Just leave that term as a variable.
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B:  In the model from part A we think of restricting the age to 15. That corresponds to putting   in the formula, so H is a function of r.  Make a graph of H versus r with . You may assume that r is no larger than 1.
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C:  Use your graph in part B to determine for what value of r the person will reach 90% of adult height at age 15.
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D:  Use the information you found in part C to make a logistic model of height versus age.
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Round your answers to two decimal places, if necessary.

What will be an ideal response?


A:

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B:

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C:  per year

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D:


Mathematics

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