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.

Recall that the average rate of change of ƒ(t) with respect to time, t, for the function ƒ as t changes from t_{1} to t_{2}, where t_{1}<t_{2}, is given by the following formula:

average rate of change = (ƒ(t_{2}) - ƒ(t_{1})) / (t_{2} - t_{1})

You are given the following:

at 10 minutes, the bell is at a depth of 400 feet (i.e., ƒ(t_{1}) = ƒ(10) = 400)

at 40 minutes, the bell is at a depth of 1900 feet (i.e., ƒ(t_{2}) = ƒ(40) = 1900)

Therefore, the average rate of change of the depth of the bell is as follows:

(ƒ(t_{2}) - ƒ(t_{1})) / (t_{2} - t_{1})

= (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)