Download Mathematical Modeling: Energy Consumption & CO2 in France - Prof. Janice Pearce and more Assignments Mathematics in PDF only on Docsity!
MAT 108 Environmental Issues: A Mathematical Modeling Approach
Earth Algebra Homework Supplement
GLOSSARY
BTU (British Thermal Unit) - Energy is often measured in BTUs in which one BTU is the amount of
energy necessary to heat one pound of water by a single degree Fahrenheit.
Next do all of the following:
- In 1985 France consumed about 6,200 Trillion BTUs of Energy. Since then France's nationwide
energy consumption has actually been going down by approximately 50 Trillion BTUs per year! (Yey
France!)
a. Assuming these trends continue, how much energy would you predict that France will consume this
year?
b. If you want to create a model from these data, you will need a dependent and an independent
variable. Let E = Energy consumption in France, and N = number of years after 1985. Which is
independent, and why?
c. Find a linear equation that can be used to represent the relationship between E, energy consumption in
France, and N, the number of years after 1985.
d. Briefly explain why this relationship must be linear.
(It's NOT a good reason to say that I said so in part c! Explain how you know that is correct.)
- Until the World War II, carbon dioxide (CO 2
) concentrations held fairly steady at about 280 parts
per million (ppm) of the atmosphere. During the World War II industrialization period, atmospheric
CO
levels began t rise. There is currently more CO 2
than any other greenhouse gas, and CO 2
is
responsible from more than 50% of the greenhouse effect. If C = 1.4 t + 320 is an equation that can be
used to model carbon dioxide concentrations, where C is carbon dioxide concentration in parts per
million (ppm), and t is the number of years after 1965, then do all of the following on a separate sheet
of paper.
a. Using this model, estimate the CO 2
concentrations in the years 1965, 1975, 1985, 1995, and 2005.
b. Using your (x, y) pairs obtained in a, sketch a graph of this model.
c. Thinking about the fact that atmospheric CO 2
trends changed during the second World war, find a
justifiable domain and range for this model. Explain your thinking.
d. In what year does this model predict that CO 2
concentrations will double the pre-World War II
level?
e. Discuss what social, political or physical changes might effect the future accuracy of this model.
