Question 714498
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 = 13.17 PSI, 
 
{{{a = ln(13.17/14.7)/-0.21}}}
 
{{{a = ln(0.895918)/-0.21}}}
 
{{{a = (-0.109906)/(-0.21)}}}
 
{{{a = 0.523362}}} miles or 2763 feet.