Accurate methods of estimating the age of gray wolves are important to scientists who study wolf population dynamics. One method of estimating the age of a gray wolf is to measure the percent closure of the pulp cavity of a canine tooth and then estimate age by

where p is the percent closure and A(p) is the age of the wolf (in years).

(a) What is a sensible domain for this function?
(b) Use differentials to estimate how long it will take for a gray wolf that first measures a 60% closure to obtain a 65% closure. Compare this with the actual value of about 0.55 year.

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A(p) = 1.181p 94.359 - p