Chapter 3.6, Problem 34E

To determine

To graph: The data using regression of logarithmic model.

Explanation of Solution

Given: The atmospheric pressure decrease with increasing altitude. At sea level, the average air pressure is approximately 1.03323 kilograms per square centimeter, and this pressure is called one atm. The ordered pair $\left(h,p\right)$ gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  $\left(0,1\right),\left(10,0.25\right),\left(20,0.06\right),\left(5,0.55\right),\left(15,0.12\right),\left(25,0.02\right)$

First plot the points on graph.

  

For logarithmic regression of h, the input value of log can’t be negative or 0.

So, can’t make any model of ordered pair $\left(h,p\right)$ .

To determine

To graph: The data using regression of logarithmic model.

Answer to Problem 34E

  $h=0.8627-6.447\ln p$

Explanation of Solution

Given: The atmospheric pressure decrease with increasing altitude. At sea level, the average air pressure is approximately 1.03323 kilograms per square centimeter, and this pressure is called one atm. The ordered pair $\left(h,p\right)$ gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  $\left(0,1\right),\left(10,0.25\right),\left(20,0.06\right),\left(5,0.55\right),\left(15,0.12\right),\left(25,0.02\right)$

First change the ordered pair and the plot it on graph.

  $\left(1,0\right),\left(0.25,10\right),\left(0.06,20\right),\left(0.55,5\right),\left(0.12,15\right),\left(0.02,25\right)$

For logarithmic regression of p, $h=0.8627-6.447\ln p$

To determine

To graph: The data using regression of logarithmic model.

Explanation of Solution

Given: The atmospheric pressure decrease with increasing altitude. At sea level, the average air pressure is approximately 1.03323 kilograms per square centimeter, and this pressure is called one atm. The ordered pair $\left(h,p\right)$ gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  $\left(0,1\right),\left(10,0.25\right),\left(20,0.06\right),\left(5,0.55\right),\left(15,0.12\right),\left(25,0.02\right)$

First change the ordered pair and the plot it on graph.

  $\left(1,0\right),\left(0.25,10\right),\left(0.06,20\right),\left(0.55,5\right),\left(0.12,15\right),\left(0.02,25\right)$

  

To determine

To find: The altitude at which the pressure is 0.75 atmosphere.

Answer to Problem 34E

2.717 km

Explanation of Solution

Given: The atmospheric pressure decrease with increasing altitude. At sea level, the average air pressure is approximately 1.03323 kilograms per square centimeter, and this pressure is called one atm. The ordered pair $\left(h,p\right)$ gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  $\left(0,1\right),\left(10,0.25\right),\left(20,0.06\right),\left(5,0.55\right),\left(15,0.12\right),\left(25,0.02\right)$

The logarithmic function of given data, $h=0.8627-6.447\ln p$

Put $p=0.75$

  $\begin{array}{l}h=0.8627-6.447\ln \left(0.75\right)\\ h=2.717\end{array}$

Hence, the altitude is 2.717 km.

To determine

To find: The pressure at an altitude of 13 km.

Answer to Problem 34E

0.1522 atm

Explanation of Solution

Given: The atmospheric pressure decrease with increasing altitude. At sea level, the average air pressure is approximately 1.03323 kilograms per square centimeter, and this pressure is called one atm. The ordered pair $\left(h,p\right)$ gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  $\left(0,1\right),\left(10,0.25\right),\left(20,0.06\right),\left(5,0.55\right),\left(15,0.12\right),\left(25,0.02\right)$

The logarithmic function of given data, $h=0.8627-6.447\ln p$

Put $h=13$

  $\begin{array}{l}13=0.8627-6.447\ln p\\ p=0.1522\end{array}$

Hence, the pressure is 0.1522 atm