Earth Math

The Gas-Mileage Bill

and

The Arctic National Wildlife Refuge

Introduction 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.

Comprehension

Questions

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 policy?

Do you think that drilling ANWR will relieve our foreign dependence on oil?
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.

Acquisition

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.

Application

Questions

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.

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.

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.

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.

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.

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.

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 2020.
What would the savings in oil be for this higher fuel efficiency?
Compare this the estimated amount of oil available from ANWR.

Reflection

Questions

What conclusions did you reach from this study?
How do you think that drilling ANWR would affect wildlife, vegetation and the pristine beauty of the area?
Do you think that there are viable alternative fuels?
How was mathematics helpful in this study?



Review Topics Exponential Functions Exponential Regression Exponential Equations
	Home / PreCalculus The Gas-Mileage Bill and The Arctic National Wildlife Refuge Introduction 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. Comprehension Questions 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 policy? Do you think that drilling ANWR will relieve our foreign dependence on oil? 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. Acquisition 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. Application Questions 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. 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. 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. 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. 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. 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. 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 2020. What would the savings in oil be for this higher fuel efficiency? Compare this the estimated amount of oil available from ANWR. Reflection Questions What conclusions did you reach from this study? How do you think that drilling ANWR would affect wildlife, vegetation and the pristine beauty of the area? Do you think that there are viable alternative fuels? How was mathematics helpful in this study? Return to Earth Math Home Page