How does air resistance affect a bullet?

I've been doing the maths on how the air resistance would affect the distance travelled by the bullet on the rifle range. I've used as the resultant force F the drag equation used in the previous post. A bit of calculus shows that the rate of change of velocity with distance depends on velocity, not velocity squared. Integration below shows that the factor is divided by mass, so maybe I've got the start of how ballistic coefficient is derived. 

If range would be when v = 0, then no proper inegral can be done because that would give the range as infinite in this model. So I have just worked on the idea that velocity decreases exponentially with distance. Mass of a .303 bullet is about 175 grams. Putting in the data I used in the last post, I made a spreadsheet to see what happened.

Over the length of the rifle range, air resistance makes very little difference so my calculation of a 5 metre drop for the bullet over the range should still stand. However I have not factored in that the bullet is supersonic.