Assignment Problem: Rate-in Rate-out Super FRQ (Calculator Active)
Coal is burning in a furnace, thus exhausting the resource. The rate at which coal is burning, measured in pounds per hour, is given by B(t) = 8sin(t/2π). At t = 2 hours a worker starts supplying additional coal into the furnace. The rate at which coal is being added, measured in pounds per hour, is given by S(t) = 11 + 10cos(4πt/25). The worker stops adding coal at t = 5 hours. At t = 0 there are 500 pounds of coal in the furnace.
(a) Find the total amount of coal, in pounds, added by the worker.
(b) Is the amount of coal in the furnace increasing or decreasing at 4 hours? Explain.
(c) Find S'(3), Explain, with units, the meaning of this in the context of the problem.
(d) Write a piecewise function A(t), that gives the total amount of coal in the furnace at any time t.
(e) Find the minimum and maximum amount of coal, in pounds, from time t = 0 to t = 5 hours and the times that they occur.
(f) Find the average rate of coal burned from t = 0 to t = 8 hours.
(g) After t = 5 hours, the coal continues to burn until there are 0 pounds of coal remaining. Write an equation involving one or more integral expressions, that gives the time t = k, that the cool is exhausted.
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