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8. On a certain workday, the rate, in tons per hour, at which unprocessed phosphorous arrives at a fertilizer plant is modeled by G) below, where t is measured in hours and 0 st 58. G(t) = 90 + 45 cos At the beginning of the workday (t = 0), the plant has 500 tons of unprocessed phosphorous. During the hours of operation, 0 st S 8, the plant processes phosphorous at a constant rate of 100 tons per hour. a.) Find G'(5). Using correct units, interpret your answer in the context of the problem. 2 points b.) Find the total amount of unprocessed phosphorous that arrives at the plant during the hours of operation on this workday. 2 points c.) Is the amount of unprocessed phosphorous at the plant increasing or decreasing at time t = 5 hours? Show the work that leads to your answer. 2 points d.) What is the maximum amount of unprocessed phosphorous at the plant during the hours of operation on this workday? Justify your answer. 3 points