Question 890812
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.