- #1

swashbuckler77

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## Homework Statement

An exponential model for the density of the earth’s atmosphere says that if the temperature of the atmosphere were constant, then the density of the atmosphere as a function of height, h (in meters), above the surface of the Earth would be given by δ(h) = 1.28e

^{(−0.000124h)}kg/m

^{3}.

Write and evaluate a sum that approximates the mass of the portion of the atmosphere from h = 0 to h = 100 m (i.e., the ﬁrst 100 meters above sea level). Assume the radius of the Earth is 6400 km.

## Homework Equations

Since this is like a density distribution problem but in three dimensions, I surmised that now, instead of using mass=2∏∫r*δ(r) dr from a to b (the circumference of a circle and the formula provided in the textbook's example problem), I will use mass=4∏∫h

^{2}*δ(h) dh, which is the surface area of a sphere with density as a function δ(h) distributed over 6400000 to 6400100, because going from circumference of a circle to surface area of a sphere seems like a logical transition from 2D to 3D.

## The Attempt at a Solution

mass=4∏∫h

^{2}*δ(h) dh from 6400000 to 6400100

=4∏∫h

^{2}*1.28e

^{(−0.000124h)}dh from 6400000 to 6400100

=5.12∏∫h

^{2}*e

^{(−0.000124h)}dh from 6400000 to 6400100

I'm unsure if I am going in the right direction because this looks like a very ugly integral with a lot of zeroes that make me rather uncomfortable.

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