Question

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

Answer 1

Answer:

The height is 1343.13 meters.

Step-by-step 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)