Water is flowing into and out of a small reservoir. The total amount of water can be modeled by R, where R(t) = 20 15 sin( t 2 25) cubic feet, t is measured in hours, and 0 t 8. a) What is the average rate of change of R over the interval 0 t 8? Indicate the correct units of measure. b) Find the value of R (2). Using correct units, interpret the meaning of the value in the context of the problem. c) Find all times t for which the rate at which the amount of water in the reservoir is changing is equal to the average rate of change of R over the interval 0 t 8. d) The reservoir can hold a maximum of 30 cubic feet. At what time after t = 8 hours will the reservoir reach its capacity?