Atmospheric pressure decreases exponentially with height

Steps:

• Pressure at height h equals weight of air column above per unit area.
• Differential equation dp/dh = -ρg relates pressure change to density ρ and gravity g.
• For ideal gas, ρ proportional to p, yielding dp/p = - (Mg/RT) dh.
• Solution is p = p₀ exp(-h/H), exponential decay with scale height H.

Why C is correct:

• Matches barometric formula p = p₀ exp(-mgh/kT), showing rapid initial drop that flattens.

Why the others are wrong:

• A: Linear decrease overpredicts drop at high altitudes.
• B: Constant pressure ignores density variation.
• D: Increasing pressure contradicts hydrostatic equilibrium.

Final answer: C