Question

Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 2 million barrels of oil in the well; six years later 1,000,000 barrels remain.

Required:
a. At what rate was the amount of oil in the well decreasing when there were 1,200,000 barrels remaining?
b. When will there be 100,000 barrels remaining?

Answer 1

A. It was decreasing by -138,629.44 barrels

B. 26 years of time

Explanation:

Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.

A. At 1200000

Bt = 1200000

-1/6ln2 x 1200000

Solve this using a calculator

= -138,629.4361

So the amount of oil is decreasing by -138,629.44 barrels