A find the height of an aircraft if the atmospheric pressure

The atmospheric pressure p on a balloon or an aircraft decreases with increasing height This pressure, measured in millimeters of mercury, is related to the height h (in kilometers) above sea level bythe formula p 0.145h 760 e (a) Find the height of an aircraft if the atmospheric pressure is344 milimeters of mercury The height of the aircraft is kilometers. (Round to two decimal places) (b) Find the height of a mountain if the atmospheric pressure is 622 millimeters of mercury The height of the mountain is kilometers. (Round to two decimal places) Enter your answer in each of the answer boxes. 3:33 PM 11/30/2016

Solution

p = 760e^(-0.145h)

a) You\'re given p, so just solve the equation for h:
p = 760e^-0.145h = 344
760/344 = e^0.145h
ln (760/344) = 0.145h
h = [ln (760/344) / 0.145]
h 5.47 km


b) Same as the previous problem:
p = 760e^-0.145h = 622
760/622 = e^0.145h
ln (760/622) = 0.145h
h = [ln (760/622) / 0.145]
h 1.382 km