How atmospheric pressure changes with altitude — model P(x) = 29.9(0.89)^x (pressure in inches of mercury per kilometer)

Interpretation of the model: P(x) = 29.9(0.89)^x gives atmospheric pressure in inches of mercury at x kilometers above sea level.

1. Sea-level pressure (x = 0): P(0) = 29.9(0.89)^0 = 29.9 inHg. That is the starting value at sea level.
2. How pressure changes with each additional kilometer: Multiply by 0.89 for each extra kilometer. Because 0.89 < 1, pressure decreases as x increases. The factor 0.89 means the pressure is 89% of the previous kilometer's pressure, i.e. it decreases by 11% per kilometer.
3. Examples:
   P(1) = 29.9(0.89) ≈ 26.61 inHg
   P(2) = 29.9(0.89)^2 ≈ 23.68 inHg
   P(5) = 29.9(0.89)^5 ≈ 16.69 inHg
4. Rate of change (calculus view): The instantaneous rate is P'(x) = 29.9(0.89)^x ln(0.89), which is negative because ln(0.89)<0, confirming a continuous exponential decrease.

Summary: Atmospheric pressure decreases exponentially with altitude according to this model, dropping by about 11% for each additional kilometer above sea level.