Question

Atmospheric pressure, measured in pounds per square inch (psi) is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, p, exerted on an airplane flying at an altitude of a miles above sea level can be approximated by the model shown below. What is the best interpretation of 0.8^a in this equation?

p = 14.63 - 0.8^a

A. If the airplane reaches the outer extent of the Earth's atmosphere, the atmospheric pressure will be 0.8 psi.

B. If the airplane is at sea level, the atmospheric pressure will be 0.8 psi.

C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

D. For each mile that the altitude increases, the atmospheric pressure increases 20%.

Answer 1

C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

Answer 2

Option D.

For each mile that the altitude increases, the atmospheric pressure increases 20%

Explanation:

Given that atmospheric pressure, measured in pounds per square inch (psi) is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, p, exerted on an airplane flying at an altitude of a miles above sea level can be approximated by the model shown below.

`p=14.63-0.8^a`

Or
`0.8^a =14.63-p\\=0.8^a ln 0.8=(-dp)/(da)`

0.2231 (0.8^a) = dp/da

Since positive sign and approximately equals 20% we have

Option D.

For each mile that the altitude increases, the atmospheric pressure increases 20%