Average Value of a Rate Function
The function $$v(t)$$ represents the rate of change of inventory in a warehouse, in items per hour, where $$t$$ is the number of hours since 8 A.M. Positive values of $$v(t)$$ indicate items are added, while negative values indicate items are removed. Which of the following best interprets the expression $$\frac{1}{11-4}\int_4^{11} v(t)\, dt$$ in this context?
A
The average rate of inventory change, in items per hour, between 12 P.M. and 7 P.M.
B
The instantaneous rate of inventory change, in items per hour, at 7 P.M.
C
The total number of items that were processed (added or removed) between 12 P.M. and 7 P.M.
D
The net change in inventory, in items, between 12 P.M. and 7 P.M.
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