On a given workday, the rate in tons per hour, at which unprocessed ore arrives

Question

On a given workday, the rate, in tons per hour, at which unprocessee ore arrives at a refinery is modeled by O (t) = 20 + 10 cos (t^2÷25) where t is measured in hours and 0 <= t <= 10. At the beginning of the workday, t = 0, the refinery has 100 tons of unprocessed ore. During the hours of operation, the refinery processes ore at a constant rate of 25 tons per hour.

(A) Find O^1(4). Usng correct units, interpret your answer in the context of the problem.

(B) How much total ore has been processed by the refinery after the plant has been open for 3 hours.

(C) Is the amount of unprocessed ore at the refinery increasing or decreasing at time t = 4 hours? Show the work that leads to your answer

(D) Determine the time at which the total rate of ore at the refinery is neither increasing nor decreasing? Justify your answer

Answer 1