Question

Air pressure may be represented as a function of height above the surface of the Earth as shown below.In this function, P0 is air pressure at sea level, and h is measured in meters. Which of the following equations will find the height at which air pressure is 65% of the air pressure at sea level?A.B.C.D.

Answer 1

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

`P=P_0e^(-0.00012h)`

Where h is the height in meters and

`P_0\text{ is the air pressure at sea level.}`

Required: To find out which equation will find the height at which air pressure is 65% of the air pressure at sea level.

Explanation: We are given that air pressure is 65% of the air pressure at sea level i.e.

`\begin{gathered} P=65\%* P_0 \\ P=0.65P_0 \end{gathered}`

Now putting this value of P in the given function we get

`0.65P_0=P_0e^(-0.00012h)`

This is equivalent to the expression given in option A.

Final Answer: Option A is correct.