Explanation Given: Oil well yields 400 barrels of crude oil Price of crude oil = $108/barrel It increases at the rate of $0.03 per barrel per month Calculation: Consider an oil well that yields 400 barrels of crude oil per month. The price of crude oil is currently $ 108 per barrel and is rising at a constant rate of $ 0.03 per barrel per month. So, the price of the crude oil after t months will be, p ( t ) = 108 + 0.03 t ......(1) Revenue function will be, R ′ ( t ) = 400 × p ( t ) = 400 ( 108 + 0.03 t ) Use the formula for the cumulative change for a quantity Q ( x ) , “If Q ′ ( x ) is the rate of change of the quantity Q ( x ) , then cumulative change for Q ( x ) over time-period [a, b] will be obtained by the definite Integral, Q ( b ) − Q ( a ) = ∫ b b Q ′ ( x ) d x ′ ′ ......(2) For 2 years, t = 12 × 2 = 24 Substitute, the values in the above expression, R ′ ( t ) 400 ( 108 + 0.03 t ) , a = 0 and b = 24

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ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.6, Problem 37PS

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To find: the total future revenue from the well

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Chapter 6.6, Problem 36PS

Chapter 6.6, Problem 38PS

Chapter 6 Solutions

Calculus

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the total future revenue from the well

Solution Summary: The author calculates the total future revenue from the well in 2 years. The price of crude oil is currently 108 per barrel and is rising at a constant rate of 0.03 per month.

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To find: the total future revenue from the well

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Chapter 6 Solutions