A graphing calculator may be used for the following problem. On a given workday, the rate, in tons per hour, at which unprocessed ore arrives at a refinery is modeled
by O(+) = 20 + 10 cos (4), where t is measured in hours and Osts 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'(4). Using 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.