# Classroom-Ready Data Sets in Environmental Math - An Extended Problem

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 full-day 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, 1974-1985

 Download the Mauna Loa atmospheric carbon dioxide (CO2) 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 CO2 will be present in the atmosphere at Mauna Loa in 2005?   De-trend 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
1. Estimate the period and amplitude of the de-trended data. Then describe the de-trended data with either a sine or cosine function.

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

3. Determine a function that describes the original data set (before de-trending).

4. Read the background information on the Mauna Loa CO2 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, "Classroom-Ready Data Sets in Environmental Math - An Extended Problem," Convergence (December 2004)

## JOMA

Journal of Online Mathematics and its Applications