Chapter 8.2, Problem 38PPSE

Solution

To identify: The location where the model predict the pressure to be about 23.93 in. of mercury. The formula $p=\frac{69.1}{a+2.3}$ models the relationship between atmospheric pressure p in inches of mercury and altitude $a$ in miles.

The options are:

  $\left(a\right)$ Sahara Desert $\left(b\right)$ Kalahari Desert

  $\left(c\right)$ Mt. Kilimanjaro $\left(d\right)$ Vinson Massif

The correct option is $\left(b\right)$ Kalahari Desert.

Given information:

The formula $p=\frac{69.1}{a+2.3}$ models the relationship between atmospheric pressure p in inches of mercury and altitude $a$ in miles.

Explanation:

Consider the given formula:

  $p=\frac{69.1}{a+2.3}$

Now find the location at which pressure of mercury is 23.93 inches by substituting the value of p as 23.93 in the formula.

  $23.93=\frac{69.1}{a+2.3}$

Now solve it,

  $\begin{array}{c}a+2.3=\frac{69.1}{23.93}\\ a=\frac{69.1}{23.93}-2.3\\ \approx 0.5875\text{miles}\\ \approx \text{0}\text{.5875}\times \text{5280}\text{ft}\\ \approx \text{3100}\text{ft}\end{array}$

Therefore, the location at which pressure of mercury is 23.93 inches is Kalahari Desert. Then the correct option should be $\left(b\right)$ Kalahari Desert.