The atmospheric pressure P in pounds per square inch (psi) is given by
Where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.27 psi, what is its altitude?

A) 2,565 ft
B) 3,038 ft
C) 2,549 ft
D) 2,573 ft
E) 2,557 ft

Question

The atmospheric pressure P in pounds per square inch (psi) is given by ​  ​
Where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.27 psi, what is its altitude?
​
A) 2,565 ft 
B) 3,038 ft 
C) 2,549 ft 
D) 2,573 ft 
E) 2,557 ft

Quizplus · Accepted Answer

Plug in the given atmospheric pressure, 13.27, for P in the equation:
13.27 = 11e^(-a/6.71)
Solve for a:
1.204 = e^(-a/6.71)
Take the natural logarithm of both sides:
ln(1.204) = -a/6.71
a = -6.71*ln(1.204) ≈ 2,573 ft 
Therefore, the answer is D) 2,573 ft.

The Atmospheric Pressure P in Pounds Per Square Inch (Psi)