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.

At what rate was the amount of oil in the well decreasing when there were 1,800,000 barrels remaining?

When will there be 150,000 barrels remaining?

Question

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.

At what rate was the amount of oil in the well decreasing when there were 1,800,000 barrels remaining? 

When will there be 150,000 barrels remaining?

amistre64 · Answer

so its a direct variation on the proportion?

anonymous · Answer

i think so...

amistre64 · Answer

dp/dv = v  might be a useful setup, but its hard to tell.  might need to include a scaling factor tho

anonymous · Answer

i set it up using y=Ce^kt. but that didn't work, when it should have ><

amistre64 · Answer

dp = av dv  integrates up to:

p = av^2/2 + C

but then i see a remark in there with respect to time so it looks like my idea needs modifications

anonymous · Answer

i won't have to integrate. the course i'm doing is solely differentiation-based. :/

amistre64 · Answer

as time passes, the volume decreases and the amount pumped decreases ... modeling was never my strong point :/

amistre64 · Answer

i dont have the benefit of your course tho, so I tend to have to work this out in my head :)

amistre64 · Answer

why didnt your way panout?

amistre64 · Answer

http://answers.yahoo.com/question/index?qid=20090222211638AAIzQBo this seems to have a similar feel to it that might help out

amistre64 · Answer

http://www-personal.umich.edu/~melsey/teaching/m116_q10_11_sln.pdf this is more along the lines of what i was thinking :)