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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.)
Replace p with 13.25, find a
Divide both sides by 14.7
Find the nat log of both sides, ln of e is 1, so we have
-.21a*1 = ln(.90136)
-.21a = -.10385
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