Chapter 11.4, Problem 65E

a.

To determine

To graph the function for atmospheric pressure.

Explanation of Solution

Given:

The atmospheric pressure $P$ (in pounds per square inch) is represented by the logarithmic function ${\log }_{2.72}\frac{p}{14.7}=-0.02h$ where $h$ is the altitude in miles.

Calculation:

Consider the function ${\log }_{2.72}\frac{p}{14.7}=-0.02h$

The following table gives the different values of P for h.

  

The following shows the graph of given equation $p=14.7\left({2.72}^{(-0.02h)}\right)$ .

  

b.

To determine

To find atmospheric pressure in Denver.

Answer to Problem 65E

  $14.5$ Pounds per square inch.

Explanation of Solution

Given:

The elevation is $1$ mile.

Calculation:

The equation is given by ${\log }_{2.72}\frac{p}{14.7}=-0.02h$

Here, $p$ is the atmospheric pressure in pounds per square inch, and $h$ is the altitude in miles.

Rearrange the equation for $p$ .

  $p=14.7\left({2.72}^{(-0.02h)}\right)$

Substitute $1$ mile for h.

  $\begin{array}{l}p=14.7\left({2.72}^{(-0.02\times 1)}\right)\\ p=14.5\end{array}$

Therefore, the atmospheric pressure is $14.5$ pounds per square inch.

c.

To determine

To find the atmospheric pressure for given elevation.

Answer to Problem 65E

  $12.8$ Pounds per square inch.

Explanation of Solution

Given:

The elevation is $6.8$ miles.

Calculation:

Substitute $6.8$ mile for $h$ .

  $\begin{array}{l}p=14.7\left({2.72}^{(-0.02\times 6.8)}\right)\\ p=12.8\end{array}$

Therefore, the atmospheric pressure is $12.8$ pounds per square inch.