miltonboss,
This altitude correction factor is based on the change in pressure with height.
The correction factor that is applied is proportional to the ratio of the air pressure at sea level over the air pressure at elevated height (ie p0/p, as you are multiplying by Ka)
It can roughly be calculated by p = p0 exp-(g.M.H/R/T0)
where
g = gravity = 9.8
M = molar mass of dry air = 0.029
H = height above sea level = the height you want the pressure at
R = gas constant = 8.31
T0 = sea level standard temperature = 288 deg K (273 + 25 degrees K)
Now if you group all the terms in the brackets, excluding the height, you get (g.M/R/T0) = (9.8*0.029/8.31/288) = roughly (1/8000).
So now P0/P = exp(m*H/8000) ish. The exponential becomes a positive because you've moved it to the other side of the equation.
The m varies with the type of voltage being applied (ie ac, dc, impulse)
So ultimately, in answer to your original question, is it an exponential due to the rate that atmospheric changes with respect to height, and the 8150 comes from that equation when you insert all the constants that go into it.
ausphil
