Question: 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/m3
(a) Write (but do not 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.
(b) Find the exact answer by turning your sum in part (a) into an integral. Evaluate the integral.