Oil Well Problem: Suppose you work for a company that plans to drill a well to a depth

Chapter 11, Problem R6

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Oil Well Problem: Suppose you work for a company that plans to drill a well to a depth of 50,000 ft, farther than anyone has ever drilled before. Your job is to estimate the cost of drilling. From historical records you find that it costs about $30 per foot to drill at the surface and about $50 per foot at a depth of 10,000 ft. a. Assume that the cost per foot, in dollars, varies exponentially with depth. Write the particular equation expressing cost per foot in terms of depth. b. The total cost of the well is the cost per foot times the depth, in feet. The cost per foot varies, so you realize that this is a job for calculus! Your boss needs the estimated cost of the well. What are you going to tell him?

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