You need to calculate the 'vacuum parabola' from muzzle to the crossing point of the 'flat trajectory' if you figure poa/poi is essentilly flat at 100m, you can interpolate the rise by using 150m drop as being the height of rise at 50m (high point for ease of calculation (friction/velocity change/spin change/gravity actually pull the high point back toward the muzzle - but using center of flat is close enough) . This changes slightly with barrel angle for drop at greater ranges. Remember as the projectile loses energy/velocity/spin, the effect of gravity increases.
Think a long tailed student's t distribution or a long tailed z distribution as the basic shape, the steep slope of the curve being the terminal side of the ballistic projection.