Question 433782: Suppose that you are a mathematician for Well Oils Production ,Inc. Your company is planning to drill a well 50,000 feet deep,deeper than anyone has ever drilled before.Your part of the project is to predict the cost of drilling the well. From previous well records,you ascertain that the price is 20$ per foot for drilling at the surface. and #30 per foot for drilling at 10,00 feet. Assume that the number of dollars per foot for drilling an oil well increases exponentially with the depth at which the drill is operating.
a. White equation expressing price per foot in terms of depth. You might find it more convenient to express depth in thousands of feet.
b. Predict the price per foot for drilling at depth of 20,30,40 and 50 thousand feet.
c. Carefully plot the graph of the price per foot versus depth. Choose scales that make the graph occupy most of the piece of the graph paper.
d. The area of the region under the graph represents the total number of dollars it costs to drill the well. You can see the reason by considering the units of this area. The vertical distance is $/ft and the horizontal distance is ft.,so the area has units A=(dollars/foot)*feet, or simply dollars. Count the number of squares in this region on your graph. Estimate fractional squares to the nearest 0.1 unit. When you study calculus, you will learn how to calculate such areas from the equation without having to count squares.
e. calculate the number of dollars corresponding to each square. For example, if the horizontal spacing is 2000 feet, and the vertical spacing is 5$/ft, then each square corresponds to (2000)(5)=$10000
f. Calculate the total cost of drilling the well.
Found 2 solutions by psbhowmick, boptop35:
Answer by psbhowmick(878)   (Show Source):
Answer by boptop35(1)  (Show Source):
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