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dP/dz = -gρ

(P = pressure, z = distance, g= acc due to grav, ρ = density)

If atmosphere can be treated as an isothermal ideal gas of constant mean molecular mass m, show that density drops exponentially with height,

ρ= [ρ0]e^-z/h

where h is a constant*

later i worked through to find it was the scale height ~8.5km but the value is unknown for this question.