Q. 102 - Precalculus Enhanced with Graphing Utilities

Question

Atmospheric Pressure The atmospheric pressure p on a balloon or plane decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the height h (in kilometers) above sea level by the function

          $p\left(h\right)=760e^{-0.145h}$

(a) Find the atmospheric pressure at a height of 2 kilometers (over a mile).
(b) What is it at a height of 10 kilometers (over 30,000 feet)?

Step-by-Step Solution

Answer

(a) $568.68mm$

(b)  $178.27mm$

Step 1.Given inforamation

Let us consider the height above sea level be h.
And the atmospheric pressure above sea level as a function of height be $p\left(h\right)=760e^{-0.145h}$

Step 2.

Let us consider height be 2 kilometers
Therefore pressure will be

$$\begin{gathered} p\left(2\right)=760e^{-0.145\times 2} \\ =760\left(7482\right) \\ =568.68mm \end{gathered}$$

Step 3.(b) What is it at a height of 10 kilometers (over 30,000 feet)?

Let us consider height be 10 kilometers
Therefore pressure will be

$$\begin{gathered} p\left(10\right)=760e^{0.145\times 10} \\ =760(0.2345) \\ =178.27mm \end{gathered}$$