The time that I'm trying to come up with is a deer's ACTUAL reaction time at a matrix of speeds/ranges. The time that passes between his hearing of the sound of the bow going off, and the arrow's impact.

Due to the time it takes for the sound to travel from bow -->deer the targetis not hearing the bow at the same instant that it's fired.

Chronologically -

Bow goes off, arrow is in flight. (some time elapses)
Deer hears bow. (more time elapses)
Deer smacked by arrow.

About the "jumping/ducking" distinction - I know - I was just trying to lead into the meat of this discussion - which is actually "Reaction Time" - and how it changes with various bow speeds.