I have done very little reading about reloading and ballistics beyond what is in the Nosler reloading manual I use. But I am sure there are some very knowledgeable folks on here who would know the answer to my questions.

I see all of these published figures for various loads that give the velocity of a bullet at given distances after it has been shot from a rifle, and so I am curious as to the original function used to take the derivative to arrive at that instantaneous change (or velocity if you will).

And then of course, they will sometimes say the total distance that the bullet will travel, and so I would imagine that they will take the integral (antiderivative) of the original function in order to arrive at that total distance.

But again, how do they come up with the original function for each bullets flight path?