PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter 7.1, Problem 45E
Solution

a.

To calculate: The linear regression models for the populations of both cities using the given data.

    Time
    (years)    		Philadelphia (thousands)Phoenix
    ( thousands)
    19801688790
    19901586983
    200015171321
    201015261446
    201515671563

The obtained matrix is y≈−3.62x+1645.64, and y≈22.41x+794.77 .

Given Information:

The table is defined,

    Time
    (years)    		Philadelphia (thousands)Phoenix
    ( thousands)
    19801688790
    19901586983
    200015171321
    201015261446
    201515671563

Calculation:

Consider the given table,

    Time
    (years)    		Philadelphia (thousands)Phoenix
    ( thousands)
    19801688790
    19901586983
    200015171321
    201015261446
    201515671563

Use a graphing calculator to find the linear rgeression.

Step 1. Insert the table in calculator by using the table feature.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 7.1, Problem 45E , additional homework tip 1

Step 2. Use the LinReg feature with first two list L1 and L2 o obtain the linear regression model for the population of Philadelphia.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 7.1, Problem 45E , additional homework tip 2

And,

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 7.1, Problem 45E , additional homework tip 3

Step 3. Use the LinReg feature with first two list L1 and L3 o obtain the linear regression model for the population of Phoenix.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 7.1, Problem 45E , additional homework tip 4

And,

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 7.1, Problem 45E , additional homework tip 5

Step 4. Use the Graph feature to plot the both the graph as scatter graph.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 7.1, Problem 45E , additional homework tip 6

Therefore, the obtained equation is y≈−3.62x+1645.64, and y≈22.41x+794.77 .

b.

To calculate: The time when the populations of the two cities were the same as well as the common population of the two cities.

The obtained result is 1526.18 thousand .

Given Information:

The equations from the previous part is y≈−3.62x+1645.64, and y≈22.41x+794.77 ,

Calculation:

Consider the given information,

Equate both the equations y≈−3.62x+1645.64, and y≈22.41x+794.77 to find that time.

  22.41x+794.77=−3.62x+1645.6422.41x+3.62x=1645.64−794.7726.03x=850.87x≈33

Add the obtained value in 1980.

  1980+33=2013

The corresponding year is 2013.

Now, substitute 33 for x in any equation.

  y≈−3.6233+1645.64=−119.46+1645.64=1526.18 thousand

Hence, the obtained result is 1526.18 thousand .

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Chapter 7.1, Problem 44E
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Chapter 7.1, Problem 46E

Chapter 7 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 7.1 - Prob. 1QRCh. 7.1 - Prob. 2QRCh. 7.1 - Prob. 3QRCh. 7.1 - Prob. 4QRCh. 7.1 - Prob. 5QRCh. 7.1 - Prob. 6QRCh. 7.1 - Prob. 7QRCh. 7.1 - Prob. 8QRCh. 7.1 - Prob. 9QRCh. 7.1 - Prob. 10QR
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - 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