Sam was 28 inches tall on her first birthday, 50 inches tall on her eighth, and 62

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Sam was 28 inches tall on her first birthday, 50 inches tall on her eighth, 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 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 long-term expected height? That is, what is lim h(t)? 00

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

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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