Author(s):
Greg Langkamp and Joe Hull
Data sets can also serve as the basis for more involved student assignments, including extended homework problems and fullday classroom activities. Here is a problem that can be used in a precalculus and trigonometry course. The data analysis can be done using WebStat, a graphing calculator, or spreadsheet software.
Atmospheric Carbon Dioxide at the Mauna Loa Observatory, 19741985

Download the Mauna Loa atmospheric carbon dioxide (CO_{2}) data provided at Data Set #016.

Determine a linear function (regression line) that describes the overall trend in the data. Graph the linear function along with the data. Interpret the meaning of the slope in the function. What concentration of CO_{2} will be present in the atmosphere at Mauna Loa in 2005?

Detrend the data, so that the linear increase is removed. Explain how you accomplish this.

The Mauna Loa Observatory with view of the dome housing Dobson ozone spectrophotometer and air intake tower for atmospheric constituent measurements. Source: NOAA Photo Library


Estimate the period and amplitude of the detrended data. Then describe the detrended data with either a sine or cosine function.

Make a plot of the residuals (i.e. differences) between the detrended data and your trigonometric function found in part 4. Are the detrended data perfectly sinusoidal? Explain.

Determine a function that describes the original data set (before detrending).

Read the background information on the Mauna Loa CO_{2} data (see About the Data). Describe how the data would be different if the Mauna Loa observatory were located in the southern hemisphere. How could you modify your functions from parts 4 and 6 so that they would fit southern hemisphere data?
Greg Langkamp and Joe Hull, "ClassroomReady Data Sets in Environmental Math  An Extended Problem," Convergence (December 2004)
Journal of Online Mathematics and its Applications