"....dont matter if it has a built in linear or not."
it's clear that the distance variable is not part of the equation and neither was it of any concern to the original poster since a radio with an amplifier will produce a STRONGER SIGNAL (UV/M) than one without. the fact that receiver sensitivity, antenna height, gain and propagation mode are able to influence the amount of energy at any given point in space from the transmitter measured in microvolts per meter has nothing whatsoever to do with the modulation index or "loudness".
in an am transmitter producing 4W of carrier and 16WPEP the increase created by the modulated envelope is 6db. and the same goes for a transmitter producing 100W of carrier and 400WPEP, 6db.. take any amount of carrier power and modulate it to four times that carrier power and you have a 100% modulated signal.
dB = 10 LOG (1 + M)2
db = 10 LOG (1 + 1)2
db = 10 LOG (2)2
db = 10 LOG (4)
db = 10 (.60)
db = 6.0
M = modulation index, 1 = 100%
the "loudness" of an am transmitter is solely based on the amount of increase in power output between carrier only and fully modulated (100%) carrier conditions, period.
if the original poster intended the distance variable to be a factor here he would not have added the statement "....dont matter if it has a built in linear or not."