More detail on my toy calculation: 
1) From NewtonII and the ram pressure formula,  F = ma = - rho A v^2 - g. 
2) The atmospheric pressure gradient is dp/dz = rho g.
3) dv/dp = dv/dt * dt/dz * dz/dp = ( a / v ) ( 1 / rho g )
4) Hence dv/dp =  ( rho A v^2 + g ) / ( m v rho g )
Neglecting the gravity term gives us
5)  dv/dp = A v / ( m g ),  so
6)  v = v(0) exp( - ( A / m g ) (p - p(0)))