The atmospheric pressure decreases with increasing altitude. At sea level, the average air pressure is one atmosphere (1.033227 kilograms per square centimeter). The table shows the pressures p (in atmospheres) at selected altitudes h (in kilometers). (a) Use a graphing utility to find a model of the form p = a + b ln h for the data. Explain why the result is an error message. (b) Use a graphing utility to find the logarithmic model h = a + b ln p for the data. (c) Use a graphing utility to plot the data and graph the model from part (b). (d) Use the model to estimate the altitude when p = 0.75. (e) Use the model to estimate the pressure when h = 13. (f) Use the model to find the rates of change of pressure when h = 5 and h = 20. Interpret the results.
![20 25
h
5
10
15
1
0.55
0.25
0.12
0.06
0.02](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbaa043b7-f109-40cb-90cc-c5d416c14593%2Fe3928cde-f5fe-4c68-93b4-ff3a2832c602%2Fl44oto6.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
We are answering only the first three subparts as per our honor code.
(a) Use a graphing utility to find a model of the form p = a + b ln h for the data. Explain why the result is an error message.
(b) Use a graphing utility to find the logarithmic model h = a + b ln p for the data.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)