Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
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Chapter 3.6, Problem 34E
To determine

To graph: The data using regression of logarithmic model.

Expert Solution
Check Mark

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 (h,p) gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  (0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)

First plot the points on graph.

  Precalculus with Limits: A Graphing Approach, Chapter 3.6, Problem 34E , additional homework tip 1

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 (h,p) .

To determine

To graph: The data using regression of logarithmic model.

Expert Solution
Check Mark

Answer to Problem 34E

  h=0.8627−6.447lnp

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 (h,p) gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  (0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)

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

  (1,0),(0.25,10),(0.06,20),(0.55,5),(0.12,15),(0.02,25)

For logarithmic regression of p, h=0.8627−6.447lnp

To determine

To graph: The data using regression of logarithmic model.

Expert Solution
Check Mark

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 (h,p) gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  (0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)

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

  (1,0),(0.25,10),(0.06,20),(0.55,5),(0.12,15),(0.02,25)

  Precalculus with Limits: A Graphing Approach, Chapter 3.6, Problem 34E , additional homework tip 2

To determine

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

Expert Solution
Check Mark

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 (h,p) gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  (0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)

The logarithmic function of given data, h=0.8627−6.447lnp

Put p=0.75

  h=0.8627−6.447ln(0.75)h=2.717

Hence, the altitude is 2.717 km.

To determine

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

Expert Solution
Check Mark

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 (h,p) gives pressures p (in atmospheres) for various altitudes h (in kilometer).

  (0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)

The logarithmic function of given data, h=0.8627−6.447lnp

Put h=13

  13=0.8627−6.447lnpp=0.1522

Hence, the pressure is 0.1522 atm

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Chapter 3.6, Problem 33E
Next
Chapter 3.6, Problem 35E

Chapter 3 Solutions

Precalculus with Limits: A Graphing Approach

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Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - Prob. 37ECh. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - Prob. 41ECh. 3.5 - Prob. 42ECh. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - Prob. 45ECh. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Prob. 56ECh. 3.5 - Prob. 57ECh. 3.5 - Prob. 58ECh. 3.5 - Prob. 59ECh. 3.5 - Prob. 60ECh. 3.5 - Prob. 61ECh. 3.5 - Prob. 62ECh. 3.5 - Prob. 63ECh. 3.5 - Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 3.5 - Prob. 67ECh. 3.5 - Prob. 68ECh. 3.5 - Prob. 69ECh. 3.5 - Prob. 70ECh. 3.5 - Prob. 71ECh. 3.5 - Prob. 72ECh. 3.5 - Prob. 73ECh. 3.5 - Prob. 74ECh. 3.5 - Prob. 75ECh. 3.5 - Prob. 76ECh. 3.5 - Prob. 77ECh. 3.5 - Prob. 78ECh. 3.5 - Prob. 79ECh. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Prob. 50RECh. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - Prob. 54RECh. 3 - Prob. 55RECh. 3 - Prob. 56RECh. 3 - Prob. 57RECh. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - Prob. 63RECh. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 68RECh. 3 - Prob. 69RECh. 3 - Prob. 70RECh. 3 - Prob. 71RECh. 3 - Prob. 72RECh. 3 - Prob. 73RECh. 3 - Prob. 74RECh. 3 - Prob. 75RECh. 3 - Prob. 76RECh. 3 - Prob. 77RECh. 3 - Prob. 78RECh. 3 - Prob. 79RECh. 3 - Prob. 80RECh. 3 - Prob. 81RECh. 3 - Prob. 82RECh. 3 - Prob. 83RECh. 3 - Prob. 84RECh. 3 - Prob. 85RECh. 3 - Prob. 86RECh. 3 - Prob. 87RECh. 3 - Prob. 88RECh. 3 - Prob. 89RECh. 3 - Prob. 90RECh. 3 - Prob. 91RECh. 3 - Prob. 92RECh. 3 - Prob. 93RECh. 3 - Prob. 94RECh. 3 - Prob. 95RECh. 3 - Prob. 96RECh. 3 - Prob. 97RECh. 3 - Prob. 98RECh. 3 - Prob. 99RECh. 3 - Prob. 100RECh. 3 - Prob. 101RECh. 3 - Prob. 102RECh. 3 - Prob. 103RECh. 3 - Prob. 104RECh. 3 - Prob. 105RECh. 3 - Prob. 106RECh. 3 - Prob. 107RECh. 3 - Prob. 108RECh. 3 - Prob. 109RECh. 3 - Prob. 110RECh. 3 - Prob. 111RECh. 3 - Prob. 112RECh. 3 - Prob. 113RECh. 3 - Prob. 114RECh. 3 - Prob. 115RECh. 3 - Prob. 116RECh. 3 - Prob. 117RECh. 3 - Prob. 118RECh. 3 - Prob. 119RECh. 3 - Prob. 120RECh. 3 - Prob. 121RECh. 3 - Prob. 122RECh. 3 - Prob. 123RECh. 3 - Prob. 124RECh. 3 - Prob. 125RECh. 3 - Prob. 126RECh. 3 - Prob. 127RECh. 3 - Prob. 128RECh. 3 - Prob. 129RECh. 3 - Prob. 130RECh. 3 - Prob. 131RECh. 3 - Prob. 132RECh. 3 - Prob. 133RECh. 3 - Prob. 134RECh. 3 - Prob. 135RECh. 3 - Prob. 136RECh. 3 - Prob. 137RECh. 3 - Prob. 138RECh. 3 - Prob. 139RECh. 3 - Prob. 140RECh. 3 - Prob. 1CTCh. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 16CTCh. 3 - Prob. 17CTCh. 3 - Prob. 18CTCh. 3 - Prob. 19CTCh. 3 - Prob. 20CTCh. 3 - Prob. 21CTCh. 3 - Prob. 22CTCh. 3 - Prob. 23CTCh. 3 - Prob. 24CTCh. 3 - Prob. 25CTCh. 3 - Prob. 26CTCh. 3 - Prob. 27CTCh. 3 - Prob. 28CTCh. 3 - Prob. 1CLTCh. 3 - Prob. 2CLTCh. 3 - Prob. 3CLTCh. 3 - Prob. 4CLTCh. 3 - Prob. 5CLTCh. 3 - Prob. 6CLTCh. 3 - Prob. 7CLTCh. 3 - Prob. 8CLTCh. 3 - Prob. 9CLTCh. 3 - Prob. 10CLTCh. 3 - Prob. 11CLTCh. 3 - Prob. 12CLTCh. 3 - Prob. 13CLTCh. 3 - Prob. 14CLTCh. 3 - Prob. 15CLTCh. 3 - Prob. 16CLTCh. 3 - Prob. 17CLTCh. 3 - Prob. 18CLTCh. 3 - Prob. 19CLTCh. 3 - Prob. 20CLTCh. 3 - Prob. 21CLTCh. 3 - Prob. 22CLTCh. 3 - Prob. 23CLTCh. 3 - Prob. 24CLTCh. 3 - Prob. 25CLTCh. 3 - Prob. 26CLTCh. 3 - Prob. 27CLTCh. 3 - Prob. 28CLTCh. 3 - Prob. 29CLTCh. 3 - Prob. 30CLTCh. 3 - Prob. 31CLTCh. 3 - Prob. 32CLTCh. 3 - Prob. 33CLTCh. 3 - Prob. 34CLTCh. 3 - Prob. 35CLTCh. 3 - Prob. 36CLTCh. 3 - Prob. 37CLTCh. 3 - Prob. 38CLTCh. 3 - Prob. 39CLTCh. 3 - Prob. 40CLTCh. 3 - Prob. 41CLTCh. 3 - Prob. 42CLTCh. 3 - Prob. 43CLTCh. 3 - Prob. 44CLTCh. 3 - Prob. 45CLTCh. 3 - Prob. 46CLTCh. 3 - Prob. 47CLT
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