At higher altitudes, the rate of air pressure decrease is characterized by a rapid decrease initially, which then slows down as altitude increases. This behavior is a result of the changing density of the atmosphere.
In the lower levels of the atmosphere, where pressure is higher, the air molecules are more densely packed, leading to a steeper gradient of pressure changes with altitude. As you ascend, the air becomes less dense, meaning that the number of air molecules that contribute to pressure decreases more gradually. Thus, the pressure decreases quickly initially due to the greater density and then begins to taper off as the density drops and the rate of pressure change becomes less pronounced.
This phenomenon aligns with the barometric formula, which describes how pressure changes with altitude in the atmosphere. The relationship reflects both the physical characteristics of the atmosphere and how the gases interact with one another as altitude increases.