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^(-0.21a)}}}
:
Replace p with 13.25, find a
{{{14.7*e^(-0.21a) = 13.25}}}
Divide both sides by 14.7
{{{e^(-0.21a) = 13.25/14.7}}}
{{{e^(-0.21a) = .90136}}}
Find the nat log of both sides, ln of e is 1, so we have
-.21a*1 = ln(.90136)
-.21a = -.10385
a = {{{(-.10385)/(.21)}}}
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