How high is the peak of the mountain?

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 8.223 pounds per square inch?

Answer 1

We can use the given equation to help us find the answer:

P = 14.7 * e^-0.21x

8.223 = 14.7 * e^-0.21x

8.223/14.7 = e^-0.21x

ln(8.223/14.7) = ln(e^-0.21x)

-0.58091238779 = -0.21x

x = 2.76624946569

So the peak has a height of approximately 2.766 miles above sea level.