air pressure decreasing exponentially

Question

Air pressure, P, decreases exponentially with the height, h, in meters above sea level:
P=P0e^-.00012h
Where P0 (p not) is the air pressure at sea level.
At a height of 5895 meters, what is the air pressure, as a percent of the pressure at sea level?

Answer 1

P₀ is called P naught.

 

P = P₀e^0.00012h

P = P₀e^{0.00012(5895)}

P ≈ P₀e^0.70

P ≈ P₀(2.0)

P/P₀ ≈ 2

 

The air pressure is 200% of that at sea level.

Answer 2

The solution by Mark M has a little problem, it shows the pressure to INCREASE with elevation instead of decreasing. A little oversight perhaps. 

 

The formula is P=P0e^-.00012h 

 

Please don't ignore the "negative" sign.

 

Rest is simple:

 

P ≈ P0e-0.7074

 

P ≈ P0(0.493)

P/P0 ≈ 0.5

 

Or, Pressure at an altitude of 5895 m is approximately half of the pressure at sea-level.