BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 4P

a.

To determine

Make a scatter plot of the data.

Expert Solution

Answer to Problem 4P

/

Explanation of Solution

Given information:

The Mauna Loa Observatory, located on the island of Hawaii, has been monitoring carbon dioxide ( CO2 ) levels in the atmosphere since 1958 . The table lists the average annual CO2 levels measured in parts per million (ppm) from 1984 to 2006 .

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 4P , additional homework tip  1

Calculation:

Consider two point P(5,2),Q(3,6) in the coordinate plane,

The scatter plot for points P(5,2),Q(3,6) is as shown,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 4P , additional homework tip  2

Hence, the function is plotted.

b.

To determine

Find and graph the regression line.

Expert Solution

Answer to Problem 4P

  y=12x92

Explanation of Solution

Given information:

The Mauna Loa Observatory, located on the island of Hawaii, has been monitoring carbon dioxide ( CO2 ) levels in the atmosphere since 1958 . The table lists the average annual CO2 levels measured in parts per million (ppm) from 1984 to 2006 .

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 4P , additional homework tip  3

Calculation:

Apply distance formula to find the distance between points P(5,2),Q(3,6) .

  PQ=(6(2))2+(35)2=(4)2+(8)2=16+64=80=8.94

Slope of line is ,

  m(slope)=6(2)35=6+28=48=12

Now the equation of line will be,

  y(2)=12(x5)y+2=12x52y=12x92

Hence, the regression line is y=12x92 .

c.

To determine

Compare the answer with the actual CO2 level of 379.7 that was measured in 2005 and part(b) data.

Expert Solution

Answer to Problem 4P

  (1,4)

Explanation of Solution

Given information:

The Mauna Loa Observatory, located on the island of Hawaii, has been monitoring carbon dioxide ( CO2 ) levels in the atmosphere since 1958 . The table lists the average annual CO2 levels measured in parts per million (ppm) from 1984 to 2006 .

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 4P , additional homework tip  4

Calculation:

The mid point of line joining P(5,2),Q(3,6) is,

  =5+(3)2,2+(6)2=532,262=22,82=1,4

Hence, the result is, (1,4) .

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