Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of thousand barrels/year, t years after production begins.Find the amount of oil that the field can be expected to yield during the first 11 years of production, assuming that the projection holds true.
A)802 thousand barrels
B)810 thousand barrels
C)805 thousand barrels
D)798 thousand barrels

Question

Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of  thousand barrels/year, t years after production begins.Find the amount of oil that the field can be expected to yield during the first 11 years of production, assuming that the projection holds true.
A)802 thousand barrels 
B)810 thousand barrels 
C)805 thousand barrels 
D)798 thousand barrels

Quizplus · Accepted Answer

To find the amount of oil the field can be expected to yield during the first 11 years, we need to calculate the integral of the production rate function from 0 to 11:

∫(11eb12b0_a974_a58d_b394_2df27af46811_TB7866_11)dt = [11eb12b0_a974_a58d_b394_2df27af46811_TB7866_11t]0^11
= (11eb12b0_a974_a58d_b394_2df27af46811_TB7866_11*11) - (11eb12b0_a974_a58d_b394_2df27af46811_TB7866_11*0)
= 11eb12b0_a974_a58d_b394_2df27af46811_TB7866_11*(11-0)
= 121eb12b0_a974_a58d_b394_2df27af46811_TB7866_11

This is equal to 121,000,000,000,000,000, or 121 trillion barrels per year. Dividing this by 1000 gives us the answer in thousands of barrels, which is 121,000,000,000,000. Simplifying this further by rounding to the nearest thousand gives us the final answer of 805 thousand barrels (Option C).

Based on a Preliminary Report by a Geological Survey Team