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Precalculus

Carbon Dioxide Concentration - Precalculus Version

Comprehension

  1. What is the greenhouse effect?
  2. Which gases are greenhouse gases?
  3. How has the concentration of atmospheric carbon dioxide changed in the last century?
  4. What are some of the effects of increased concentration of carbon dioxide?
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The graph shown provides information about the atmospheric concentration of carbon dioxide since 1960, measured in parts per million. (http://cdiac.esd.ornl.gov/trends/co2/graphics/sio-mlgr.gif)
Questions
  1. What trends do you observe from the data?
  2. Do you think these trends will continue in the near future?
  3. What kinds of functions (linear, quadratic, exponential, etc.) would accurately describe the change in atmospheric CO<2 concentration over the last 40 years?
  4. On the average, how much is the concentration changing each year?
Acquisition

Mathematical Topics
Learn or review mathematical concepts and skills needed to study trends in atmospheric CO2 concentration. See the menu at the left.
Application
Apply mathematical concepts and use appropriate technology to analyze past trends. 
Information
The table below provides information on carbon dioxide concentration for selected years.   
Year 1960 1965 1970 1975 1980 1985 1990 1995 2000
Concentration (ppm) 316.75 319.87 325.52 330.99 338.52 345.73 354.04 360.91 369.40
Questions
1.      For convenience, we will let t denote years since 2000; that is, t=0 in 2000.  Let C denote the carbon dioxide concentration. Make points out of the data and plot them; use a (t,C) coordinate system.
2.      Use exponential regression to fit the data with a linear function.  Call this function C(t) and graph it.
3.     For each of the years you have data provided, compare the actual carbon dioxide concentration with the concentration predicted by your function.  Why do you think the figures are different?
4.     Use the function C(t) to answer these questions.

a.      Estimate the carbon dioxide concentration in 2001.

b.      Predict when the carbon dioxide concentration will reach 400 PPM

c.     How much did carbon dioxide concentration increase between January 1, 1990 and January 1 19991? between January 2000 and January 1 2001? between January 1, 1990 and January 1, 2000?

The annual change in carbon dioxide concentration for year t is

The total change in carbon dioxide concentration between times t = a and t = b is

The average annual change in carbon dioxide concentration between times t = a and t = b is

5. Compute the following:

a. The annual change in concentration for 2001.

b. The change in concentration between times t = 0 and t = 5.

c. The average annual change in concentration between t = 0 and t = 5.

6. Until recently, the carbon dioxide concentration stayed at about 280 PPM 

a.  According to your model, when was the concentration at this level? 

b.  When will the concentration reach double that level?

Save this information.  You will use it in part II
Reflection
1. Reflect on the computation:

a. What did you do to predict carbon dioxide concentration at a particular time?
b. What did you do to predict when the concentration reached a particular level?

2. Reflect on the graph:

a. Which do you think is greater: the time it takes for the concentration to increase from 280 PPM to 330 PPM or the time it takes to increase from 330 PPM to 380 PPM? Why do you think that is?
b. How is the graph different from the graph of a linear function? How is it similar?

3. Reflect on the interpretations:

a. What factors might cause a change in the trend you observed?
b. For how far into the future do you think your model is accurate?

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