Search 83,321 tutors
FIND TUTORS
Ask a question
0 0

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.

Tutors, please sign in to answer this question.

1 Answer

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)