Question 890812: where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 11.19 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you need the formula for atmospheric pressure in terms of altitude.
the formula is normally shown as P = 14.7 * e^(-.21*a).
if your formula is different because they take 14.7 out to more decimal places, then you need to use what you are given instead.
P is the atmospheric pressure.
a is the altitude in miles.
in your problem, P is given as 11.19 and you want to solve for a.
the equation becomes:
11.19 = 14.7 * e^(-.21*a)
divide both sides of this equation by 14.7 to get:
11.19 / 14.7 = e^(-.21*a)
take the natural log of both sides of this equation to get:
ln(11.19/14.7) = ln(e^(-.21*a)
since ln(e^(-.21*a) is equal to -.21*a*ln(e), your equation becomes:
ln(11.19/14.7) = -.21*a*ln(e)
since ln(e) = 1, your equation becomes:
ln(11.19/14.7) = -.21*a
divide both sides of this equation by -.21 to get:
ln(11.19/14.7)/-.21 = a
solve for a to get:
a = 1.299176... miles
since there are 5280 feet in a mile, then you get:
a = 6859.6495... feet which you can round to 6860 feet.
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