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.

If is the amount of oil in the well (let's say in millions of barrels) at time

for some negative value of . You're told that the well started off with 3 million barrels, so , and that after 6 years, there are 1.5 million barrels, so .

Solve the differential equation above:



Integrate both sides.






Given that and , you have



So the amount of oil in the well is given by the function