Question 714501
Starting with the original equation:
 
{{{P = 14.7e^(-0.21a)}}}
 
Where P is the atmospheric pressure in PSI, and a is the altitude in miles.  We're given P and need to solve for a.
 
{{{P = 14.7e^(-0.21a)}}}
 
{{{P/14.7 = e^(-0.21a)}}}
 
{{{ln(P/14.7) = ln(e^(-0.21a))}}}
 
{{{ln(P/14.7) = -0.21a}}}
 
{{{ln(P/14.7)/-0.21 = a}}}
 
So for P = 11.27 PSI, 
 
{{{a = ln(11.27/14.7)/-0.21}}}
 
{{{a = ln(0.766667)/-0.21}}}
 
{{{a = (-0.265703)/(-0.21)}}}
 
{{{a = 1.265253}}} miles or 6681 feet.