For t > 8, water continues to flow into and out of the pipe at the given rates until the pipe begins to overflow. (d) The pipe can hold 50 cubic feet of water before overflowing. (c) At what time t, 0 ≤ t ≤ 8, is the amount of water in the pipe at a minimum? Justify your answer. (b) Is the amount of water in the pipe increasing or decreasing at time t 3 hours? Give a reason for your answer.
(a) How many cubic feet of rainwater flow into the pipe during the 8-hour time interval 0 ≤ t ≤ 8?
There are 30 cubic feet of water in the pipe at time t = 0. The pipe is partially blocked, allowing water to drain out the other end of the pipe at a rate modeled by D(t) = -0.04t 3 + 0.4t 2 + 0.96t cubic feet per hour, for 0 ≤ t ≤ 8.
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