PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Concept explainers

Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…
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Question
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Chapter 3.6, Problem 31E

(a)

To determine

To find: The linear model of the data.

(a)

Expert Solution
Check Mark

Answer to Problem 31E

  P=0.0136t+2.6607

Explanation of Solution

Given:The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with t−1 corresponding to 2001.

  Year200120022003200420052006200720082009201020112012201320142015t2345678910111213141516Population,P2.6772.6952.7132.7292.7452.7602.7752.7902.8042.8172.8292.8412.8522.8622.872

Using regression graphing calculator, the linear model of the above data is P=0.0136t+2.6607

The coefficient of determination is r2=0.9911

Now plot the model and data on same window view.

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.6, Problem 31E , additional homework tip 1

(b)

To determine

To find: The power model of the data.

(b)

Expert Solution
Check Mark

Answer to Problem 31E

  P=2.584t0.0364

Explanation of Solution

Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with t−1 corresponding to 2001.

  Year200120022003200420052006200720082009201020112012201320142015t2345678910111213141516Population,P2.6772.6952.7132.7292.7452.7602.7752.7902.8042.8172.8292.8412.8522.8622.872

Using regression graphing calculator, the power model of the above data is P=2.584t0.0364 .

The coefficient of determination is r2=0.9655 .

Now plot the model and data on same window view.

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.6, Problem 31E , additional homework tip 2

(c)

To determine

To find: The exponential model of the data.

(c)

Expert Solution
Check Mark

Answer to Problem 31E

  P=2.6627(1.0049)x

Explanation of Solution

Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with t−1 corresponding to 2001.

  Year200120022003200420052006200720082009201020112012201320142015t2345678910111213141516Population,P2.6772.6952.7132.7292.7452.7602.7752.7902.8042.8172.8292.8412.8522.8622.872

Using regression graphing calculator, the exponential model of the above data is P=2.6627(1.0049)x .

The coefficient of determination is r2=0.9891 .

Now plot the model and data on same window view.

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.6, Problem 31E , additional homework tip 3

(d)

To determine

To find: The logarithmic model of the data.

(d)

Expert Solution
Check Mark

Answer to Problem 31E

  P=0.101ln(t)+2.5786

Explanation of Solution

Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with t−1 corresponding to 2001.

  Year200120022003200420052006200720082009201020112012201320142015t2345678910111213141516Population,P2.6772.6952.7132.7292.7452.7602.7752.7902.8042.8172.8292.8412.8522.8622.872

Using regression graphing calculator, the logarithmic model of the above data is P=0.101ln(t)+2.5786

The coefficient of determination is r2=0.962

Now plot the model and data on same window view.

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.6, Problem 31E , additional homework tip 4

(e)

To determine

To find: The model which is best fit for data.

(e)

Expert Solution
Check Mark

Answer to Problem 31E

Linear Model

Explanation of Solution

Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with t−1 corresponding to 2001.

  Year200120022003200420052006200720082009201020112012201320142015t2345678910111213141516Population,P2.6772.6952.7132.7292.7452.7602.7752.7902.8042.8172.8292.8412.8522.8622.872

Linear model, P=0.0136t+2.6607 .

Power model, P=2.584t0.0364 .

Exponential model, P=2.6627(1.0049)x .

Logarithmic model, P=0.101ln(t)+2.5786 .

The coefficient of determination of linear model is nearest 1.

So, Best fir model would be linear model.

(f)

To determine

To find: The population in year 2025 of each model.

(f)

Expert Solution
Check Mark

Answer to Problem 31E

For linear model population in Jamaica is 3.014

For power model population in Jamaica is 2.909

For exponential model population in Jamaica is 3.024

For logarithmic model population in Jamaica is 2.908

Explanation of Solution

Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with t−1 corresponding to 2001.

  Year200120022003200420052006200720082009201020112012201320142015t2345678910111213141516Population,P2.6772.6952.7132.7292.7452.7602.7752.7902.8042.8172.8292.8412.8522.8622.872

For 2025 corresponding value of t=26 .

Put t=26 in each model.

Linear model, P=0.0136(26)+2.6607=3.014 .

Power model, P=2.584(26)0.0364=2.909 .

Exponential model, P=2.6627(1.0049)26=3.024 .

Logarithmic model, P=0.101ln(26)+2.5786=2.908 .

(g)

To determine

To predict: The best fir model for population in year 2025.

(g)

Expert Solution
Check Mark

Answer to Problem 31E

Power model

Explanation of Solution

Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with t−1 corresponding to 2001.

  Year200120022003200420052006200720082009201020112012201320142015t2345678910111213141516Population,P2.6772.6952.7132.7292.7452.7602.7752.7902.8042.8172.8292.8412.8522.8622.872

For 2025 corresponding value of t=26 .

Put t=26 in each model.

Linear model, P=0.0136(26)+2.6607=3.014 .

Power model, P=2.584(26)0.0364=2.909 .

Exponential model, P=2.6627(1.0049)26=3.024 .

Logarithmic model, P=0.101ln(26)+2.5786=2.908 .

According to above calculation best model is power model.

(h)

To determine

To choose: The model different for different cases.

(h)

Expert Solution
Check Mark

Answer to Problem 31E

No

Explanation of Solution

Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with t−1 corresponding to 2001.

  Year200120022003200420052006200720082009201020112012201320142015t2345678910111213141516Population,P2.6772.6952.7132.7292.7452.7602.7752.7902.8042.8172.8292.8412.8522.8622.872

For 2025 corresponding value of t=26 .

Put t=26 in each model.

Linear model, P=0.0136(26)+2.6607=3.014 .

Power model, P=2.584(26)0.0364=2.909 .

Exponential model, P=2.6627(1.0049)26=3.024 .

Logarithmic model, P=0.101ln(26)+2.5786=2.908 .

According to above calculation best model is power model.

According to graph best model is linear because the coefficient of determination is nearest to 1 but according to calculation model is different because data may be vary.

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Chapter 3.6, Problem 30E
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Chapter 3.6, Problem 32E

Chapter 3 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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Prob. 98ECh. 3.4 - Prob. 99ECh. 3.4 - Prob. 100ECh. 3.4 - Prob. 101ECh. 3.4 - Prob. 102ECh. 3.4 - Prob. 103ECh. 3.4 - Prob. 104ECh. 3.4 - Prob. 105ECh. 3.4 - Prob. 106ECh. 3.4 - Prob. 107ECh. 3.4 - Prob. 108ECh. 3.4 - Prob. 109ECh. 3.4 - Prob. 110ECh. 3.4 - Prob. 111ECh. 3.4 - Prob. 112ECh. 3.4 - Prob. 113ECh. 3.4 - Prob. 114ECh. 3.4 - Prob. 115ECh. 3.4 - Prob. 116ECh. 3.4 - Prob. 117ECh. 3.4 - Prob. 118ECh. 3.4 - Prob. 119ECh. 3.4 - Prob. 120ECh. 3.4 - Prob. 121ECh. 3.4 - Prob. 122ECh. 3.4 - Prob. 123ECh. 3.4 - Prob. 124ECh. 3.4 - Prob. 125ECh. 3.4 - Prob. 126ECh. 3.4 - Prob. 127ECh. 3.4 - Prob. 128ECh. 3.4 - Prob. 129ECh. 3.4 - Prob. 130ECh. 3.4 - Prob. 131ECh. 3.4 - Prob. 132ECh. 3.4 - Prob. 133ECh. 3.4 - Prob. 134ECh. 3.4 - Prob. 135ECh. 3.4 - Prob. 136ECh. 3.4 - Prob. 137ECh. 3.4 - Prob. 138ECh. 3.4 - Prob. 139ECh. 3.4 - Prob. 140ECh. 3.4 - Prob. 141ECh. 3.4 - Prob. 142ECh. 3.4 - Prob. 143ECh. 3.4 - Prob. 144ECh. 3.4 - Prob. 145ECh. 3.4 - Prob. 146ECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - 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. 3.6 - 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 - Prob. 1CRCh. 3 - Prob. 2CRCh. 3 - Prob. 3CRCh. 3 - Prob. 4CRCh. 3 - Prob. 5CRCh. 3 - Prob. 6CRCh. 3 - Prob. 7CRCh. 3 - Prob. 8CRCh. 3 - Prob. 9CRCh. 3 - Prob. 10CRCh. 3 - Prob. 11CRCh. 3 - Prob. 12CRCh. 3 - Prob. 13CRCh. 3 - Prob. 14CRCh. 3 - Prob. 15CRCh. 3 - Prob. 16CRCh. 3 - Prob. 17CRCh. 3 - Prob. 18CRCh. 3 - Prob. 19CRCh. 3 - Prob. 20CRCh. 3 - Prob. 21CRCh. 3 - Prob. 22CRCh. 3 - Prob. 23CRCh. 3 - Prob. 24CRCh. 3 - Prob. 25CRCh. 3 - Prob. 26CRCh. 3 - Prob. 27CRCh. 3 - Prob. 28CRCh. 3 - Prob. 29CRCh. 3 - Prob. 30CRCh. 3 - Prob. 31CRCh. 3 - Prob. 32CRCh. 3 - Prob. 33CRCh. 3 - Prob. 34CRCh. 3 - Prob. 35CRCh. 3 - Prob. 36CRCh. 3 - Prob. 37CRCh. 3 - Prob. 38CRCh. 3 - Prob. 39CRCh. 3 - Prob. 40CRCh. 3 - Prob. 41CRCh. 3 - Prob. 42CRCh. 3 - Prob. 43CRCh. 3 - Prob. 44CRCh. 3 - Prob. 45CRCh. 3 - Prob. 46CRCh. 3 - Prob. 47CRCh. 3 - Prob. 48CRCh. 3 - Prob. 49CRCh. 3 - Prob. 50CRCh. 3 - Prob. 51CRCh. 3 - Prob. 52CRCh. 3 - Prob. 53CRCh. 3 - Prob. 54CRCh. 3 - Prob. 55CRCh. 3 - Prob. 56CRCh. 3 - Prob. 57CRCh. 3 - Prob. 58CRCh. 3 - Prob. 59CRCh. 3 - Prob. 60CRCh. 3 - Prob. 61CRCh. 3 - Prob. 62CRCh. 3 - Prob. 63CRCh. 3 - Prob. 64CRCh. 3 - Prob. 65CRCh. 3 - Prob. 66CRCh. 3 - Prob. 67CRCh. 3 - Prob. 68CRCh. 3 - Prob. 69CRCh. 3 - Prob. 70CRCh. 3 - Prob. 71CRCh. 3 - Prob. 72CRCh. 3 - Prob. 73CRCh. 3 - Prob. 74CRCh. 3 - Prob. 75CRCh. 3 - Prob. 76CRCh. 3 - Prob. 77CRCh. 3 - Prob. 78CRCh. 3 - Prob. 79CRCh. 3 - Prob. 80CRCh. 3 - Prob. 81CRCh. 3 - Prob. 82CRCh. 3 - Prob. 83CRCh. 3 - Prob. 84CRCh. 3 - Prob. 85CRCh. 3 - Prob. 86CRCh. 3 - Prob. 87CRCh. 3 - Prob. 88CRCh. 3 - Prob. 89CRCh. 3 - Prob. 90CRCh. 3 - Prob. 91CRCh. 3 - Prob. 92CRCh. 3 - Prob. 93CRCh. 3 - Prob. 94CRCh. 3 - Prob. 95CRCh. 3 - Prob. 96CRCh. 3 - Prob. 97CRCh. 3 - Prob. 98CRCh. 3 - Prob. 99CRCh. 3 - Prob. 100CRCh. 3 - Prob. 101CRCh. 3 - Prob. 102CRCh. 3 - Prob. 103CRCh. 3 - Prob. 104CRCh. 3 - Prob. 105CRCh. 3 - Prob. 106CRCh. 3 - Prob. 107CRCh. 3 - Prob. 108CRCh. 3 - Prob. 109CRCh. 3 - Prob. 110CRCh. 3 - Prob. 111CRCh. 3 - Prob. 112CRCh. 3 - Prob. 113CRCh. 3 - Prob. 114CRCh. 3 - Prob. 115CRCh. 3 - Prob. 116CRCh. 3 - Prob. 117CRCh. 3 - Prob. 118CRCh. 3 - Prob. 119CRCh. 3 - Prob. 120CRCh. 3 - Prob. 121CRCh. 3 - Prob. 122CRCh. 3 - Prob. 123CRCh. 3 - Prob. 124CRCh. 3 - Prob. 125CRCh. 3 - Prob. 126CRCh. 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. 29CTCh. 3 - Prob. 30CTCh. 3 - Prob. 1STPCh. 3 - Prob. 2STPCh. 3 - Prob. 3STPCh. 3 - Prob. 4STPCh. 3 - Prob. 5STPCh. 3 - Prob. 6STPCh. 3 - Prob. 7STPCh. 3 - Prob. 8STPCh. 3 - Prob. 9STPCh. 3 - Prob. 10STPCh. 3 - Prob. 11STPCh. 3 - Prob. 12STPCh. 3 - Prob. 13STPCh. 3 - Prob. 14STPCh. 3 - Prob. 15STPCh. 3 - Prob. 16STPCh. 3 - Prob. 17STPCh. 3 - Prob. 18STPCh. 3 - Prob. 19STPCh. 3 - Prob. 20STPCh. 3 - Prob. 21STPCh. 3 - Prob. 22STPCh. 3 - Prob. 23STPCh. 3 - Prob. 24STPCh. 3 - Prob. 25STPCh. 3 - Prob. 26STP
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