How much will the atmospheric pressure decrease if the terrain is 9 km high?

760 mmHg Art. – standard atmospheric pressure at sea level.
When you rise approximately every 10.5 meters above sea level, the pressure drops by 1 mm Hg. Art., but at such high altitudes as 9 km, this dependence is violated.
We use the formula:
P = P0 * e ^ (- Mgh / RT),
where P0 – atmospheric pressure at sea level, e = 2.7183, M – molar mass of dry air, M = 0.029 kg / mol, g –
gravity acceleration, g = 9.81 m / s², h – height, m, R – universal gas constant, R = 8.31 J / mol · K, T – absolute air temperature, K, T = t + 273, 15, where t = – 40 (approximately) is the Celsius temperature expressed in degrees Celsius (symbol: ° C).
P = 760 * 2.7183 ^ (- 0.029 * 9.81 * 9000 / 8.31 * (- 40 + 273.15)) = 760 * 2.7183 ^ (- 2560.41 / 1937.4765) = 760 * 2.7183 ^ (- 1.3215) = 760 / 2.7183 ^ 1.3215 = 760 / 3.7491 = 202.716 mm Hg. Art.
760 – 202.716 = 557.284 (mmHg)
Answer: at 557, 284 mm Hg. Art.