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Tcecarenko [31]
3 years ago
11

Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 3 mill

ion barrels of oil in the well; six years later 1,500,000 barrels remain.
(a) At what rate was the amount of oil in the well decreasing when there were 1,800,000 barrels remaining?
Mathematics
1 answer:
abruzzese [7]3 years ago
4 0

Answer:

V' = -0.11552 *V\\= -0.11552(1.8)\\ \\=-0.20794 million per year

Step-by-step explanation:

Given that oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 3 million barrels of oil in the well; six years later 1,500,000 barrels remain.

i.e. if V stands for volume of oil, then

V' =kV\\dv/V= kdt\\ln V = kt+C\\V = Ae^{kt}

To find A and k

V(0) = A = 3 million

Hence V = 3e^{kt}

V(6) = 1.5

i.e. 1.5 = 3e^{6k}\\ln 1.5 =ln 3 +6k\\k = -0.11552

V(t) = 3e^{-0.11552t}

a) Using the above value of k , we have

V' = -0.11552 *V\\= -0.11552(1.8)\\ \\=-0.20794 million per year.

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