Question

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 8.743 pounds per square inch?

Answer 1

9514 1404 393

Answer:

13064 feet

Explanation:

We can rewrite the formula so that x is in feet. Equating the new formula to 8.743 PSI, we have ...

8.743 = 14.7e^(-0.21x/5280)

Dividing by 14.7 and taking natural logs, we have ...

ln(8.743/14.7) = -0.21x/5280

Multiplying by the inverse of the coefficient of x gives ...

x = 5280·ln(8.743/14.7)/-0.21 ≈ 13064.0806

The peak of the mountain is about 13,064 feet high.