3. An exponential model for the density of the Earth\'s atmosphere says that if

Question

3. An exponential model for the density of the Earth's atmosphere says that if the temperature of the atmosphere is constant, then the density of the atmosphere as a function of height h (in meters) above the surface of the Earth is given by ?(h) = 1.28e?0.000124h kg/m3. Find the total mass of the portion of the atmosphere from h = 0 to h = 100 meters. Assume that the radius of the Earth is 6370 kilometers.

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Explanation / Answer

total mass =volume*density

                  =intgeral ( 1.28*e^(-0.000124h) * pi*(6370*1000)^2 *dh) from h=0 to 100

                    =1.274*10^14*(-0.000124)*1.28*e^(-0.000124h) from h=0 to 100

                   =-2.02*10^10 * [ e^(0.000124*100)-1]

                      =-2.02*10^10*(0.9876-1)

                       =2.5*10^8kg

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