## Calculating oil drilling cost with Differential equation

Limits, differentiation, related rates, integration, trig integrals, etc.
TheAngryMathStudent
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### Calculating oil drilling cost with Differential equation

Oil drilling cost P for an oil well of depth X. A standard modell says that the rate of the drillingcost increases proportional With the drillingcost between 400m and 6000m

dp / dx = AP

where A is the proportional constant.

Given the cost of a 500m Oil well is 0,3 mill dollar and that 4 000 m cost 4,1 million dollar estimate how much it will cost to drill 6 000 meter.

I've haven't tried anything since I don't really know where to start. Can someone please help me out, pref with a step-by-step solution. I've tried using online calculator to try to get a vague idea of how it works, but I didn't make any use of it.

Any help is really appreciated.

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Calculating oil drilling cost with Differential equation

I've haven't tried anything since I don't really know where to start. Can someone please help me out, pref with a step-by-step solution.
You already saw a bunch of step by steps in your book, class and online. Another step by step isn't going to make a change.
Oil drilling cost P for an oil well of depth X. A standard modell says that the rate of the drillingcost increases proportional With the drillingcost between 400m and 6000m

dp / dx = AP

where A is the proportional constant.

Given the cost of a 500m Oil well is 0,3 mill dollar and that 4 000 m cost 4,1 million dollar estimate how much it will cost to drill 6 000 meter.
I don't know what language that was written in originally but I'm not sure it makes sense. This is what I guess it's supposed to be:
The cost P of drilling an oil well is defined in terms of the depth x in meters. One standard cost model says that the drilling cost increases at a rate which is proportional to that cost for depths between 400m and 6,000m. The model is dP/dx = AP, where A is the proportionality constant.

Given that a 500m-deep well costs \$0.3m and that a 4,000m-deep well costs \$4.1m, estimate the cost for drilling a well to 6,000 meters.
Please ask somebody who's good with English if this is a good translation. Thanks.