6.5=14.7e^-0.21x

Question

The formula p=14.7e^-0.21x gives the average atmospheric pressure p, in pounds per square inch, at an altitude x, in miles above sea level. Find the elevation of a jet if the atmospheric pressure outside the jet is 6.5 Ib/in^2. The elevation of the jet is approximently how much miles?

Answer 1

Putting p=6.5 into the equation: 6.5=14.7e^-0.21x.

 

e^-0.21x=6.5/14.7;

taking natural logs: -0.21x=ln(6.5/14.7)=-0.8160 so x=3.89 miles approx.