Tamara J. answered • 04/05/13
Math Tutoring - Algebra and Calculus (all levels)
Recall that the average rate of change of ƒ(t) with respect to time, t, for the function ƒ as t changes from t1 to t2, where t1<t2, is given by the following formula:
average rate of change = (ƒ(t2) - ƒ(t1)) / (t2 - t1)
You are given the following:
at 10 minutes, the bell is at a depth of 400 feet (i.e., ƒ(t1) = ƒ(10) = 400)
at 40 minutes, the bell is at a depth of 1900 feet (i.e., ƒ(t2) = ƒ(40) = 1900)
Therefore, the average rate of change of the depth of the bell is as follows:
(ƒ(t2) - ƒ(t1)) / (t2 - t1)
= (ƒ(40) - ƒ(10))/ (40 - 10)
= (1900 - 400) / 30
= 1500 / 30
= 50
Thus, the average rate of change of the depth of the bell is 50 feet per minute (i.e., 50 ft/min)
