Math 163 Applied Project
- Carbon Dioxide Emissions
Carbon emissions contribute to climate change, which has serious consequences for humans and their environment. According to the U.S. Environmental Protection Agency, carbon emissions, in the form of carbon dioxide (CO2), make up more than 80 percent of the greenhouse gases emitted in the United States (EPA, 2019). The burning of fossil fuels releases CO2 and other greenhouse gases. These carbon emissions raise global temperatures by trapping solar energy in the atmosphere. This alters water supplies and weather patterns, changes the growing season for food crops, and threatens coastal communities with increasing sea levels (EPA, 2016).
The amount of CO2 emitted per year A (in tons) for a vehicle that averages x miles per gallon of gas, can be approximated by the function .
- Interpret the interval [20, 25] in the context of the question and then calculate and interpret the average rate of change.
Determine the average rate of change of the amount of CO2 emitted in a year over the interval [35, 40], and interpret its meaning.
Provide an interpretation of the difference between the values found in parts a) and b) and state the implications in the context of vehicle emissions of CO2. Be sure to discuss what the difference is between the average miles per gallon of 20-25 versus 35-40. Is one more ideal? Provide an explanation of your reasoning. (Department of Energy, 2019)
- 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 |
(Source: U.S. Department of Commerce/National Oceanic & Atmospheric Administration. https://www.esrl.noaa.gov/gmd/ccgg/trends/data.html )
- 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 (round the slope and y-intercept values to three decimal places). Use Desmos or Excel (directions are included in this assignment) 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.
Sea-Level Rise
The Arctic ice cap is a large sheet of sea ice that contains an estimated 680,000 cubic miles of water. If the global climate were to warm significantly as a result of the greenhouse effect or other climactic change, this ice cap would start to melt (NASA, n.d.). More than 200 million people currently live on land that is less than 3 feet above sea level. There are several large cities in the world that have a low average elevation, including Miami, Florida (pop. 463,347) at 7 feet, Shanghai, China (pop. 24,180,000) at 13 feet, and Boston, Massachusetts (pop. 685,094) at 14 feet. In this part of the project you are going to estimate the rise in sea level if the ice cap were to melt and determine whether this event would have a significant impact on the people living in these three cities (US Government, 2019).
- The surface area of a sphere is given by the expression , where is its radius. Although the shape of the earth is not exactly spherical, it has an average radius of 3,960 miles. Estimate the surface area of the earth to the nearest million square miles.
Oceans cover approximately 71% of the total surface area of the earth. How many square miles of the earth’s surface are covered by oceans (again, rounded to the nearest million)?
Approximate the potential sea-level rise if half the Arctic ice cap were to melt. This can be done by dividing the volume of water from the melted ice cap by the surface area of the earth’s oceans. Convert your answer into feet.
Discuss what your approximation of the potential sea-level rise implies for the cities of Miami, Boston, and Shanghai. What are some possible social, economic, or political impacts for these cities and the people who live there? Based on your specified impact, what could be an appropriate and ethical response?
The Antarctic ice cap contains approximately 6,300,000 cubic miles of water. Approximate the potential sea-level rise if half the Antarctic ice cap were to melt, and discuss the implications for the cities of Miami, Boston, and Shanghai.
