The Arctic National Wildlife Refuge
The U.S. Senate recently defeated a bill that would require automobiles
and light trucks to have an average gasoline efficiency of 36 miles
per gallon by the year 2005. Amazingly, this comes in the wake of
the September 11 terrorist acts and this administration’s pronounced
goal to relieve our country’s dependence on foreign oil. One alternative
that the President and Secretary of Interior strongly proposed is
the offshore drilling of the Arctic National Wildlife Refuge. However,
the bill proposing this action was defeated in the Senate, but there
are still rumblings from constituents to renew the fight to drill.
This Earth Math Module explores the feasibility of this action.
- What do you
think the current average gasoline efficiency is for cars and
light trucks? (Website)
- How much
oil do you think we get from the Middle East? (Website)
- How much
oil do you think we get from North America? (Website)
- Do you think
that big U.S. oil companies have any influence on governmental
- Do you
think that drilling ANWR will relieve our foreign dependence
- Do you
think that raising gasoline efficiency will relieve our foreign
dependence on oil?
- Which do
think will have a better, longer-lasting effect?
- How do you
think mathematics could help decide this question?
- Write a plan
that you think might be used to analyze this question so that
you could make an intelligent decision.
Information you need to study this issue
The acquisition of oil is obviously dependent on money, i.e., the
price of oil. It must be profitable for oil companies to extract
the oil after the cost of labor, transportation, construction of
facilities, wells, roads, airstrips, and pipelines. The United States
Geological Survey (U.S.G.S.) has projected that at $24 a barrel,
there is a 95% possibility of extracting 1.9 billion barrels of
oil (BBO) from ANWR. Further, there is a 50% chance of obtaining
5.3 BBO, and at the maximum, a 5% chance of getting 9.4 BBO. At
less than $16 a barrel, there would be no economically recoverable
oil from ANWR.
Following the construction and preparation for drilling ANWR, extracted
oil would not be available for use until the year 2010.
The year 2000 oil consumption in the U.S. was estimated to be 7
BBO and the U.S. Dept. of Energy projects a 1.4% increase each year
through the year 2020. Cars and light trucks are responsible for
approximately 40% of our oil consumption.
Oil imports amounted to approximately 3.8 BBO in the year 2000.
Finally, it takes one barrel (40 gallons) of oil to produce approximately
20 gallons of gasoline.
Assume for the
moment that it was decided to drill ANWR, and that all oil imports
are ceased as soon as oil is available from ANWR—recall, this would
be the year 2010.
- Write the
expression that defines the exponential function that can be used
to predict the annual U.S. oil consumption from 2000 through 2020.
Denote this function by C(t), where t = 0 in the year 2000.
- What percent
of year 2000 oil consumption is imported?
- Assume the
percentage of imported oil in year 2000 remains constant through
2020. Write the expression that defines the function that can
be used to predict annual imported oil (in BBO) from 2000 through
2020. Denote this function by F(t), where t = 0 in 2000.
Now, let’s approach
this issue from a different direction—gasoline efficiency. One crucial
part of this study is the determination of the annual oil for gasoline
consumption by light trucks and cars in the U.S.; this is estimated
to be 40% of the total U.S. Oil usage.
- How much
oil would need to be extracted from ANWR in 2010 to make up the
deficit? In 2011? In 2012? How do these figures compare to the
amount of oil available from ANWR?
- Suppose we
assume the 50% estimate of oil available from ANWR. How long would
it take to use all the ANWR oil? Answer the same question for
the 5% scenario. And also for the 95% scenario.
The 40% estimate
is based on the current average fuel efficiency of approximately 17
mpg. Suppose that the gas mileage bill had been enacted, i.e., that
fuel efficiency were 36 miles per gallon.
- Write the
function G(t) which gives the annual oil for gasoline consumption
by light trucks and cars in the U.S. in year 2000 + t.
- Use the function
G(t) to estimate the amount of oil used for gasoline by light
trucks and cars from 2010 through 2020.
- What is the
percentage savings that 36 mpg represents over 17 mpg?
- Use your
answers to #7 and 8 to determine the amount of oil that would
be used for gasoline by light trucks and cars from 2010 through
- What would
the savings in oil be for this higher fuel efficiency?
- Compare this
the estimated amount of oil available from ANWR.
conclusions did you reach from this study?
do you think that drilling ANWR would affect wildlife, vegetation
and the pristine beauty of the area?
you think that there are viable alternative fuels?
was mathematics helpful in this study?