Question

Atmospheric pressure P

 in pounds per square inch is represented by the formula P=14.7e^−0.21x

where x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.163

pounds per square inch? Hint: There are 5280 feet in a mile.

Answer 1

We have to use the equation P=14.7e^−0.21x which is equivalent to:

$P=14.7\exp{(−0.21x)} \\ \therefore x = \frac{1}{0.21}\ln{(\frac{14.7}{P})}= \frac{1}{0.21}\ln{(\frac{14.7}{8.163})} \\ \text{ } \\ x=2.8011\,miles\, (\frac{5280\,ft}{1\,mile})=14789.8\,ft$

In conclusion, the peak of the mountain has an approximate height of 14790 ft.