EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
3rd Edition
ISBN: 9781285607160
Author: Larson
Publisher: CENGAGE CO
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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.
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Chapter 3, Problem 15PS

a.

To determine

To calculate: The exponential model for the data.

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

a.

Expert Solution
Check Mark

Answer to Problem 15PS

The exponential model is y=252602.75(1.36)t .

Explanation of Solution

Given information:

The population estimates of the American colonies from 1700 to 1780 is provided below,

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

Calculation:

Consider the population estimates of the American colonies from 1700 to 1780 is provided below,

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

It is provided that y represent the population in the year t with t=0 that corresponds to 1700.

Follow the steps provided below to estimate the exponential model.

Step 1: Press STAT key.

Step 2: Press ENTER key.

Step 3: Enter the column 1 of table provided above in L1 and press ENTER key.

Step 4: Enter the column 2 of table provided above in L2 and press ENTER key.

Step 5: Press 2nd key and MODE key.

Step 6: Press STAT key, select the CALC menu.

Step 7: Select the fourth option that is ExpReg and press ENTER key.

Step 8: Press 2nd key and press 1 to call list L1 and put comma.

Step 9: Press 2nd key and press 2 to call list L2 and press ENTER key.

The result obtained on screen is provided below.

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 15PS , additional homework tip 1

Therefore, exponential model is,

  y=abxy=252602.75(1.36)t

b.

To determine

To calculate: The quadratic model for the data.

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

b.

Expert Solution
Check Mark

Answer to Problem 15PS

The quadratic model is y=40090.152t2−14649.545t+291776.97 .

Explanation of Solution

Given information:

The population estimates of the American colonies from 1700 to 1780 is provided below,

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

Calculation:

Consider the population estimates of the American colonies from 1700 to 1780 is provided below,

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

It is provided that y represent the population in the year t with t=0 that corresponds to 1700.

Follow the steps provided below to estimate the quadratic model.

Step 1: Press STAT key.

Step 2: Press ENTER key.

Step 3: Enter the column 1 of table provided above in L1 and press ENTER key.

Step 4: Enter the column 2 of table provided above in L2 and press ENTER key.

Step 5: Press 2nd key and MODE key.

Step 6: Press STAT key, select the CALC menu.

Step 7: Select the fourth option that is ExpReg and press ENTER key.

Step 8: Press 2nd key and press 1 to call list L1 and put comma.

Step 9: Press 2nd key and press 2 to call list L2 and press ENTER key.

The result obtained on screen is provided below.

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 15PS , additional homework tip 2

Therefore, quadratic model is,

  y=ax2+bx+cy=40090.152t2−14649.545t+291776.97

c.

To determine

To graph: The models for the data.

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

c.

Expert Solution
Check Mark

Explanation of Solution

Given information:

The population estimates of the American colonies from 1700 to 1780 is provided below,

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

Graph:

Consider the population estimates of the American colonies from 1700 to 1780 is provided below,

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

The exponential model is y=252602.75(1.36)t .

The quadratic model is y=40090.152t2−14649.545t+291776.97 .

Plot the data points and all the models in the coordinate plane.

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 15PS , additional homework tip 3

The green curve line represents y=252602.75(1.36)t , red curve represents y=40090.152t2−14649.545t+291776.97 black curve represents the data.

Interpretation:

All the models and the data points itself coincide with each other. All the models fits with the data.

d.

To determine

To explain: The model that best fits the. Also the model that best fits the data can be used to predict the population of United Sates in 2018.

d.

Expert Solution
Check Mark

Answer to Problem 15PS

The model that best fits the data is exponential model. No, this cannot be used to predict the population.

Explanation of Solution

Given information:

The population estimates of the American colonies from 1700 to 1780 is provided below,

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

Calculation:

Consider the population estimates of the American colonies from 1700 to 1780 is provided below,

  YearPopulation1700250,9001710331,7001720466,2001730629,4001740905,60017501,170,80017601,593,60017702,148,40017802,780,400

The quadratic model is y=40090.152t2−14649.545t+291776.97 .

The exponential model is y=252602.75(1.36)t .

From the graphs it is clear that exponential model coincide with actual data points.

Exponential model cannot be used to predict the population as exponential function is increasing function and values obtained would be very high.

There would be a very high growth rate.

Thus, the model that best fits the data is exponential model. No, this cannot be used to predict the population.

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Chapter 3, Problem 14PS
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Chapter 3, Problem 16PS

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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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. 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. 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. 1PSCh. 3 - Prob. 2PSCh. 3 - Prob. 3PSCh. 3 - Prob. 4PSCh. 3 - Prob. 5PSCh. 3 - Prob. 6PSCh. 3 - Prob. 7PSCh. 3 - Prob. 8PSCh. 3 - Prob. 9PSCh. 3 - Prob. 10PSCh. 3 - Prob. 11PSCh. 3 - Prob. 12PSCh. 3 - Prob. 13PSCh. 3 - Prob. 14PSCh. 3 - Prob. 15PSCh. 3 - Prob. 16PSCh. 3 - Prob. 17PSCh. 3 - Prob. 18PSCh. 3 - Prob. 19PSCh. 3 - Prob. 20PSCh. 3 - Prob. 21PSCh. 3 - Prob. 22PSCh. 3 - Prob. 23PSCh. 3 - Prob. 24PSCh. 3 - Prob. 25PSCh. 3 - Prob. 26PS
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