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[answered] Linear Modeling Project MTH 1100 Beginning Algebra 100 poin


The text below the graph indicates that the rise and fall of the line is due to seasonal activity related to the Northern Hemisphere. Explain what this means and why this graphic is literally a display of the Earth ?breathing?. [6 points]Fit a trend-line to this graph using pencil and paper (and a ruler if needed) and compute the equation of the line. Interpret the slope in real world terms. [7 points]

See attached file

3. Compute the total change of CO2 from 1960 to 1990, the percent change, and the average change. [7 points]

4. The graphic above seems to be indicating a linear increase in CO2. Tacking this graphic onto ice core records of CO2 over the last 1000 years gives us a new perspective in the graphic below. Is it accurate to say CO2 has been increasing linearly over the last millennium? [7 points]


Linear Modeling Project

 

MTH 1100 Beginning Algebra

 

100 points

 

https://www3.epa.gov/climatechange/kids/documents/carbon-through-theseasons.pdf

 

Directions: You will explore an important application of linear equations. An important

 

application is called linear modeling. Linear modeling is helpful in looking at data that appears

 

to have a linear relationship and building what?s called a line of best-fit. This line of best-fit can

 

be used to make predictions of future events.

 

You should submit your work as one Microsoft Word file. Be sure to fully explain and answer the

 

questions. Also, show your work involved. To be able to fully show your work, you may need to:

 

use screen shots, scan a hand-written document, import from Excel, etc. This should be a full

 

report and will take some time.

 

Incoherent sloppy answers will not be tolerated. Full sentences and proper grammar is

 

expected. Not following these guidelines will result in a reduction in points. Answer your

 

questions below in this document and submit your word file to the appropriate location in

 

Canvas by the due date.

 

Resources that may be helpful: Insert a chart from an Excel spreadsheet into Word.

 

How to create a scatter diagram in Excel.

 

How to find the line of best-fit in Excel. Part A: Global Warming (60 points)

 

Global warming has received a lot of attention lately, and is now referred to as climate

 

change. The following graphic from Al Gore?s An Inconvenient Truth shows the rise

 

of Carbon Dioxide in the atmosphere as measured at Mauna Loa: Page 1 of 5 1. The text below the graph indicates that the rise and fall of the line is due to

 

seasonal activity related to the Northern Hemisphere. Explain what this means

 

and why this graphic is literally a display of the Earth ?breathing?. [6 points]

 

While the seasons change, a process called photosynthesis occurs.

 

During the growth of plants and trees in the spring and summer, more

 

carbon dioxide is produced. In months like fall and winter when the leaves

 

are falling, less carbon dioxide is produced.

 

2. Fit a trend?line to this graph using pencil and paper (and a ruler if needed) and

 

compute the equation of the line. Interpret the slope in real world terms. [7

 

points]

 

See attached file

 

3. Compute the total change of CO2 from 1960 to 1990, the percent change, and the

 

average change. [7 points]

 

4. The graphic above seems to be indicating a linear increase in CO2. Tacking this

 

graphic onto ice core records of CO2 over the last 1000 years gives us a new

 

perspective in the graphic below. Is it accurate to say CO2 has been increasing linearly

 

over the last millennium? [7 points] Page 2 of 5 The following graphic from a paper[1] by Robinson, Robinson, and Soon (available

 

here[2]) displays the average US Surface Temperatures measured over the

 

20th century along with a measure of solar activity (sunspot activity among others). These scientists are claiming that temperature variation is correlated with solar

 

activity. Solar activity is measured in Watts per square meter, i.e. energy we receive

 

from the sun per unit area.

 

[1] ?Environmental Effects of Increased Atmospheric Carbon

 

Dioxide? by Arthur B. Robinson, Noah E. Robinson, and Willie

 

Soon(Robinson et al. paper published in Journal of American Physician and

 

Surgeons (2007) 12, 79-90)

 

[2] http://www.oism.org/pproject/s33p36.htm Page 3 of 5 5. By how much has the US surface temperature warmed, according to the trend?line

 

given in the graphic, over the last century? What is the percent change? [6 points]

 

6. Use the facts that 0C = 32F and 100C = 212F to find the equation of the line

 

between the two points (0, 32) and (100, 212). [7 points]

 

7. Use the linear equation to convert your answer from part 5 to degrees

 

Fahrenheit.

 

[6 points]

 

8. Notice the US experienced a warming trend from 1900 to 1940, cooled off from 1940

 

to 1975, and warmed up again from 1975 to 2000. Ignoring solar activity, sketch a

 

trend-line for US surface temps for each of these three time periods and estimate

 

the equation of each line. [7 points]

 

9. Interpret the slopes for each line in real world terms and convert each

 

slope to degrees Fahrenheit per year. [7 points] Page 4 of 5 Part B: Linear Modeling with Excel (40 points)

 

The table lists the winning times for the women?s 400-meter freestyle swim for the Olympics.

 

Year

 

1924

 

1928

 

1932

 

1936

 

1948

 

1952

 

1956

 

1960

 

1964

 

1968

 

1972

 

1976

 

1980

 

1984 Time

 

(min:sec.)

 

06:02.2

 

05:42.8

 

05:28.5

 

05:26.4

 

05:17.8

 

05:12.1

 

04:54.6

 

04:50.6

 

04:43.3

 

04:31.3

 

04:19.0

 

04:09.9

 

04:08.8

 

04:07.1 1. Using 1920 as the base year (lowest x-value), create a scatter diagram with the ordered

 

pair (year, time). [7 points]

 

2. Graph the line of best-fit on top of your scatter diagram. [7 points]

 

3. Use excel to calculate the line of best-fit. What is the equation? [7 points]

 

4. Use the equation from #2 to predict what the times might have been if the Olympics had

 

been held in 1940 and 1944. [7 points]

 

5. Is it reasonable to use this line to predict the winning times for the 1988 Summer

 

Games? Why or why not? [7 points]

 

6. Look up the winning time for the 400-meter freestyle swim in the 1988 Summer Games

 

and compare it to the time predicted by the best-fit line. [5 points] Page 5 of 5

 


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