Water is flowing into and out of a small reservoir. The total amount of water can be modeled by R, where R(t)=20-15sin(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?