Define the number of years that have passed after 1960 as the predictor variable x, and the mean CO2 measurement for a particular year as y. Create a linear model for the mean CO2 level in the atmosphere, y = mx + b, using the data points for 1960 and 2015 .

Carbon Dioxide Change
As humans continue to burn fossil fuels, the amount of CO2 in the atmosphere increases. Scientists measure atmospheric CO2 in parts per million (ppm), which means the number of CO2 molecules for every one million molecules of other atmospheric gases such as oxygen and nitrogen. Scientists have been tracking the amount of CO2 in the atmosphere at the Mauna Loa Observatory in Hawaii since 1958.
The table below shows the CO2 measurements recorded for the years 1959-2018.
Year Mean Year Mean Year Mean Year Mean Year Mean
1959 315.97 1972 327.45 1985 346.12 1998 366.70 2011 391.65
1960 316.91 1973 329.68 1986 347.42 1999 368.38 2012 393.85
1961 317.64 1974 330.18 1987 349.19 2000 369.55 2013 396.52
1962 318.45 1975 331.11 1988 351.57 2001 371.14 2014 398.65
1963 318.99 1976 332.04 1989 353.12 2002 373.28 2015 400.83
1964 319.62 1977 333.83 1990 354.39 2003 375.80 2016 404.24
1965 320.04 1978 335.40 1991 355.61 2004 377.52 2017 406.55
1966 321.38 1979 336.84 1992 356.45 2005 379.80 2018 408.52
1967 322.16 1980 338.75 1993 357.10 2006 381.90
1968 323.04 1981 340.11 1994 358.83 2007 383.79
1969 324.62 1982 341.45 1995 360.82 2008 385.60
1970 325.68 1983 343.05 1996 362.61 2009 387.43
1971 326.32 1984 344.65 1997 363.73 2010 389.90
Use these data to make a summary table of the mean CO2 level in the atmosphere as measured at the Mauna Loa Observatory for the years 1960, 1965, 1970, 1975, …, 2015.

Define the number of years that have passed after 1960 as the predictor variable x, and the mean CO2 measurement for a particular year as y. Create a linear model for the mean CO2 level in the atmosphere, y = mx + b, using the data points for 1960 and 2015 . Use Desmos or Excel to sketch a scatter plot of the data in your summary table and also to graph the linear model over this plot. Comment on how well the linear model fits the data.

Looking at your scatter plot, choose two years that you feel may provide a better linear model than the line created in part b). Use the two points you selected to calculate a new linear model and use Desmos to plot this line as well. Provide this linear model and state the slope and y-intercept, again, rounded to three decimal places.

Use the linear model generated in part c) to predict the mean CO2 level for each of the years 2010 and 2015, separately. Compare the predicted values from your model to the recorded measured values for these years. What conclusions can you reach based on this comparison?

Again, using the linear model generated in part c), determine in which year the mean level of CO2 in the atmosphere would exceed 420 parts per million.

 

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