SOLUTION: The atmospheric pressure P in pounds per square inch (psi) is given by P = 14.7 e−0.21 a where a is the altitude above sea level (in miles). If a city has an atmospheri

Algebra ->  Rational-functions -> SOLUTION: The atmospheric pressure P in pounds per square inch (psi) is given by P = 14.7 e−0.21 a where a is the altitude above sea level (in miles). If a city has an atmospheri      Log On


   

Question 714498: The atmospheric pressure P in pounds per square inch (psi) is given by
P = 14.7 e−0.21 a
where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.17 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with the original equation:

P+=+14.7e%5E%28-0.21a%29

Where P is the atmospheric pressure in PSI, and a is the altitude in miles. We're given P and need to solve for a.

P+=+14.7e%5E%28-0.21a%29

P%2F14.7+=+e%5E%28-0.21a%29

ln%28P%2F14.7%29+=+ln%28e%5E%28-0.21a%29%29

ln%28P%2F14.7%29+=+-0.21a

ln%28P%2F14.7%29%2F-0.21+=+a

So for P = 13.17 PSI,

a+=+ln%2813.17%2F14.7%29%2F-0.21

a+=+ln%280.895918%29%2F-0.21

a+=+%28-0.109906%29%2F%28-0.21%29

a+=+0.523362 miles or 2763 feet.