Earth's atmospheric pressure is produced by the mass of the air in the atmosphere, most of which exists in the lowest 50km of the atmosphere. Earth's atmosphere at ground level produces a pressure of 101000Pa. You want to test a hypothesis that the density of air decreases exponentially to 0.1% of the sea level value by 48.6km altitude. Thus, the density would be parametrized as p(z) = Poe-z/a, where z is the altitude, and a is a decay constant. The total mass of the atmosphere above a rectangle of area A can be solved via: m = pAdz Zi If considering the entire atmosphere, then, the integration bounds are 0 to oo: 00 -z/adz | Apoe m = What is the value of a in the parametrization? km What is the force produced on a 1m2 area the atmosphere? N Assuming that the gravitational constant, g = 9.8m/s², does not change appreciably with altitude, what is the total mass of air that produces this pressure? (Note: By the time g has changed much, there is hardly any air density anyways, so it is a reasonable approximation to make for these purposes.) kg