ulator For time 0

acor For time 0 < t < 10, water is flowing into a smallt a a rate given by the function F defined by F(t) = tan For time 5 t < 10, water is leaking from the tub at a rate given by the function L defined by L(t) = 0.04(20t t2 75). Both F(t) and L(t) are measured in cubic feet per minute, and t is measured in minutes. The volume of water in the tub, in cubic feet, at time t minutes is given by W (t). (a) At time t = 3, there are 2.5 cubic feet of water in the tub. Write the equation Of the line tangent to W at t 3, and use it to approximate the volume of the water in the tub at time t 3.5. (b) Find W Using the correct units, interpret the meaning of W "(8) in the context of the problem. (c) Is there a time t, for 5 < t < 10, at which the rate of change of the volume of water in the tub changes from positive to negative? Give a reason for your answer. (d) The tub is in the shape of a rectangular box that is 0.5 feet wide, 8 feet long, and 3 feet deep. What is the rate of change of the depth of the water in the tub at time t 6?