Question

Air pressure may be represented as a function of height above the surface of

the Earth as shown below.
P(h) = P.e-.000121
In this function, Pois air pressure at sea level, and his measured in meters.
Which of the following equations will find the height at which air pressure is
85% of the air pressure at sea level?

Answer 1

The height is 1343.13 meters.

Explanation:

Air pressure may be represented as a function of height h in meters above the surface of Earth as shown below :

`P(h) = P. e^(-0.000121h)` ......... (1)

In this function, P is air pressure at sea level and h is measured in meters.

Let at a height of h meters the pressure is 85% of the sea level pressure.

Hence, from equation (1), we get

`0.85 = e^(- 0.000121 h)`

Taking ln both sides, we can write

ln 0.85 = -0.000121 h (ln e) {Since
`\ln a^(b) = b \ln a`}

⇒ h = 1343.13 meters (Answer)