1) At a processing plant, over the course of an 8-hour day, workers move material into a pile, which is removed at a constant rate by a conveyor belt. The workers move material into the pile at rate 200e^{−0.5t }units/hr while the conveyor belt removes the material at 50 units/hr.

(a) Find the net change in the size of the pile over the first 2 hours, and over the first 8 hours. Round your answers to the nearest hundredth.

2 hours =

8 hours =

(b) At what time is the amount of material in the pile the largest and the smallest?

largest t=

smallest t=

2) Consider the region in the first quadrant bounded by the line 8x−y= 0 and the curve 8x^^{3}−y= 0.

Find the volume of the solid of revolution generated by revolving this region about the linex= −1

using the disk/washer method.

Thanks!!!!