I'm stuck on parts c and d. For part c I was able to solve it but I don't understand when they say show that the density obeys a similar equation. I was able to get the p(z) equation but I don't know how to show that that equation obeys a similar equation.

and for part d I was able to solve that too but I don't know if I did that right because I didn't use the temperature or the average molecular weight m.

my p. de KI called the barometric equation. (c) Assuming that the temperature of the atmosphere is independent of height (not a great assumption but not terrible either), solve the barometric equa- tion to obtain the pressure as a function of height: P(z) = P(0)e-maz/kT Show also that the density obeys a similar equation. (d) Estimate the pressure, in atmospheres, at the following locations: Ogden, Utah (4700 ft or 1430 m above sea level); Leadville, Colorado (10, 150 ft, 3090 m); Mt. Whitney, California (14,500 ft, 4420 m); Mt. Everest, Nepal Tibet. (29,000 ft, 8850 m). (Assume that the pressure at sea level is I atm. ) (P(0) at sea level z = 0 is 1 atm, and let T - 280 K. Air is ~80% N, and 20% O2, from which you can estimate the average molecular weight m.) CA msi