Calculating oil drilling cost with differential equation

[TheAngryMathStudent]

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.

 

[stapel]

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.

You already have loads of worked examples in your textbook, in your class lecture notes, and in all those online lessons you've studied. If they've left you completely lost, then one more worked example isn't likely to make any difference. It's time to get your hands dirty in "learning by doing".

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.

Note: "P" and "p" are NOT the same variable; nor are "X" and "x". Pick one of each, or else explain how the different variables are related.

Let's start at the beginning. You've been given a statement of proportionality, and you've been given a formula. Do you understand what "proportional" means? Do you understand the equation at all? Thank you!