SOLUTION: The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, where a is the altitude above sea level (in miles). If a city has an atmospheric pressure

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Question 470925: The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.25 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
P = 14.7 e^(-0.21 a)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The atmospheric pressure P in pounds per square inch (psi) is given by the formula below,
where a is the altitude above sea level (in miles).
If a city has an atmospheric pressure of 13.25 psi, what is its altitude?
(Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
P+=+14.7%2Ae%5E%28-0.21a%29
:
Replace p with 13.25, find a
14.7%2Ae%5E%28-0.21a%29+=+13.25
Divide both sides by 14.7
e%5E%28-0.21a%29+=+13.25%2F14.7
e%5E%28-0.21a%29+=+.90136
Find the nat log of both sides, ln of e is 1, so we have
-.21a*1 = ln(.90136)
-.21a = -.10385
a = %28-.10385%29%2F%28.21%29
a = .4945 miles, which is: .4945*5280 = 2611 ft altitude
;
:
Check your solution on a calc,
enter 14.7*e^(-21*.4945) results: 13.250 psi; confirms our solution of a=2611 ft