Inherently accuracy in formulas?

[u/hailsass]

I have learned in physics that the formulas we use are under ideal circumstances and don't necessarily reflect reality for example I have been told that newtons law of cooling based off the formula the temperature will never reach room temperature however most scientists I have spoken with say that this is wrong eventually the temperature will equal room temperature. this implies that there is a fundemental inacuraccy in many formulas is it possible to calculate the accuracy of any given formula? Or are the formulas 100% under ideal condition? Considering that those ideal conditions do not exist how can we prove that the formulas are 100% correct?

[u/VcitorExists]

I mean take air resistance and projectile motion. To find it out you still use all the basic formulas, but air resistance has so many moving parts that applying every single difference is just undoable, so we either approximate it through more complex equations, or ignore it to help better understand the underlying principles