A model for the density of the earths atmosphere near its surface is 619 09 0 000097 where (the distance from the center of the earth) is measured in meters and is measured in kilograms per cubic meter If we take the surface of the earth to be a sphere with radius 6370 km, then this model is a reas...

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A model for the density of the earths atmosphere near its surface is = 619.09

Question:

A model for the density δ of the earth’s atmosphere near its surface is

δ = 619.09 − 0.000097ρ

where ρ (the distance from the center of the earth) is measured in meters and δ is measured in kilograms per cubic meter. If we take the surface of the earth to be a sphere with radius 6370 km, then this model is a reasonable one for 6.370 × 10⁶ ≤ ρ ≤ 6.375 × 10⁶. Use this model to estimate the mass of the atmosphere between the ground and an altitude of 5 km.