Free Response 2013 #1 1. On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel processing plant (13). where 1 is measured in hours and 0 18. At the beginning of the workday (t = 0), the plant has 500 tons of unprocessed gravel. During the hours of operation, 0 8, the plant processes gravel at a constant rate of 100 tons per hour. is modeled by G(1) = 90 + 45 cos (d) What is the maximum amount of unprocessed gravel at the plant during the hours of operation on this workday? Justify your answer. On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel processing plant is modeled by G(1)= 90 + 45 cos( s(f), where t is measured in hours and 0 8. At the beginning of the workday (f = 0), the plant has 500 tons of unprocessed gravel. During the hours of operation, 0 8, the plant processes gravel at a constant rate of 100 tons per hour. I a. Find G' (5). Using correct units, interpret your answer in the context of the problem. b. Is the amount of unprocessed gravel at the plant increasing or decreasing at time / = 5 hours? Show the work that leads to your answer. c. By weight, the plant processes gravel at a rate of 100 tons per hour and a ton of gravel occupies a volume of 19 cubic feet. Processed gravel is poured into a conical pile such that the ratio of the height to the radius is 2 to 3. The volume of a cone, V, is given by V = h. Identify by label (P, Q, R, S, or T) which of the following equations would be appropriate to use to find the rate of change, with respect to time, of the radius of the conical pile for a given radius. Then, find the rate of change, with respect to time, of the radius of the conical pile when the radius is 10 feet. Be sure to provide all values used in your computation. dV P. = df (2rh+r)= O R. df = 2/3 2 df alt s. fo av = 2 far T. So dV = 3 hah dt d. Let t = H hours be the time during the workday (0 t 8) when G(t) = 100. N(t) = 20(t - H)sin (7). or state that it does not exist. Justify your answer. Find lim 1-H G(1)-100 N(t) For this question, you can type "LIM" to indicate the limit as I approaches H, even though this representation does not specify that I approaches H. For example, LIM((G(t)-100)/N(t)) will be interpreted to mean lim 1-H G(1)-100 N(1) -10).