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# word problem

A deep sea diving bell is being lowered at a constant rate.  After 10 minutes, the bell is at a depth of 400 ft. After 40 minutes the bell is at a depth of 1900 ft. What is the average rate of change of depth? round to one decimal place.

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Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
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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)
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