Preview Activity 6.4.1. A bucket is being lifted from the bottom of a 50-foot deep well; its weight (includ ing the water), B, in pounds at a height 11 feet above the water is given by the function B(h). When the bucket leaves the water, the bucket and water together weigh 3(0) = 20 pounds, and when the bucket reaches the top of the well, 3(50) = 12 pounds. Assume that the bucket loses water at a constant rate (as a function of height, h) throughout its journey from the bottom to the top of the well. a. Find a formula for B(h). b. Compute the value of the product B (5)Ah, where Ah = 2 feet. Include units on your answer. Explain why this product represents the approximate work it took to move the bucket of water from h = 5 to h = 7. c. Is the value in (b) an over or under-estimate of the actual amount of work it took to move the bucket from h = 5 to h = 7? Why? d. Compute the value of the product B(22)Ah, where Ah = 0.25 feet. Include units on your answer. What is the meaning of the value you found? e. More generally, what does the quantity Wsnce = B(h)Ah measure for a given value of h and a small positive value of Ah? f. Evaluate the definite integral 1650 301) dh. What is the meaning of the value you nd? Why