Questions

What
trends do you observe from the data?

Do
you think these trends will continue in the near future?

What
kinds of functions (linear, quadratic, exponential, etc.) would
accurately describe the change in atmospheric _{CO<2} concentration over the
last 40 years?

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 CO_{2}
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?
Continue
to Next Part