• construction of 38,000 miles of new natural gas pipelines
  
  
• easing regulations that have slowed down the permitting and building of power plants and oil refineries
  
  
• tax incentives to promote the use of solar panels on residential homes and to develop alternative fuels such as biomass and methane from landfills
  
  
• opening federal lands to oil and gas exploration.

Few people would disagree that the United States needs a long-term energy strategy. Oil consumption is expected to increase by 33% over the next 20 years. Natural gas consumption will increase by more than 50%. In a year when gasoline prices skyrocketed and concerns over wars in the Middle East making us more aware of our reliance on imported oil, it is hard to argue that energy shouldn't be a topic on the national agenda.

Since the President's plan was announced, many people have criticized it as being too focused on increasing supply and not focused enough on decreasing demand — or even slowing the annual rate of increase in energy consumption. One such critic is Prof. Evar Nering, professor emeritus of mathematics at Arizona State University. In an opinion piece originally published in The New York Times, Prof. Nering explains that the energy debate reminds him of lectures he used to give to his calculus classes:

"When I discussed the exponential function in the first-semester calculus classes that I taught, I invariably used consumption of nonrenewable natural resource as an example. [...] I described the following hypothetical situation. We have a 100-year supply of a resource, say oil — that is, the oil would last 100 years if it were consumed at its current rate. But the oil is consumed at a rate that grows by 5 percent each year. How long would it last under these circumstances? This is an easy calculation; the answer is about 36 years. Oh, but let's say we underestimated the supply, and we actually have a 1,000-year supply. At the same annual 5 percent growth rate of use, how long will it last? The answer is about 79 years."

Prof. Nering goes on to show that increasing the oil supply to one that would last 10,000 years at the current rate of consumption would only last 125 years with the ever-increasing rate of consumption. Clearly, increasing supply is not the only solution.

What about conservation? How does the same exponential function operate when efforts are made to decrease oil consumption? Here is what Prof. Nering says:

"Calculations also show that if consumption of an energy resource is allowed to grow at a steady 5 percent annual rate, a full doubling of the available supply will not be as effective as reducing the growth rate by half — to 2.5%. Doubling the size of the oil reserve will add at most 14 years to the life expectancy of the resource if we continue to use it at the currently increasing rate, no matter how large it is. On the other hand, halving the growth of consumption will almost double the life expectancy of the supply, no matter what it is."

Is it possible that the mathematics behind supply and demand have escaped the politicians in Washington? Take your students on a closer look into the power of exponents.

You can start to familiarize students with exponents using the following Riverdeep activities. (The Destination Math activities require either the Destination Math CD-ROM or a Riverdeep math or full-acccess subscription. Get a free trial subscription.)

• Compound interest is an example of exponential growth. But many students may need to learn or review the concepts behind simple interest before they can tackle compound interest. Have your students do the tutorial and workouts in Calculating Simple Interest, a session from Destination Math, Mastering Skills & Concepts IV.

• Students can learn about powers and exponents in the tutorial, Working with Powers, from Destination Math, Mastering Algebra I: Course 2.

1. Think about this imaginary example, which illustrates some of the ideas behind exponential growth. Suppose that your school has its own oil-burning electrical generator. Today — day one — it is using oil at a rate of 100 barrels per day. However, the demand for energy in your school is increasing at a constant rate of 10% each day. Tomorrow you will need 10% more oil than the 100 barrels you needed today. That is, you will need 100 barrels + (10% of 100 barrels) = 100 barrels + 10 barrels = 110 barrels. How much oil will you need on the third day? Continue calculating your energy needs until you have data for 15 days. Graph your data on a graph where "number of days" is plotted along the x-axis and "number of barrels" is plotted along the y-axis. Make your graph such that the y-axis goes up to at least 1000 barrels.
   
   
2. Next, let's say that your school isn't just increasing its demand for energy by a constant 10% each day. No, in fact the demand for oil increases by an additional 1% each day. Therefore, the increase on day two is 10%, the increase on day three is 11%, day four is 12%, and so on. Calculate the amount of oil needed on each of the 15 days and plot this data on the same graph as before. Could you plot all of your data on your graph? Why not? Describe the differences between the two graphs. The second graph demonstrates what happens with exponential growth.
   
   
3. Finally, let's investigate the effects of conservation. What would happen if everyone in your school were careful and tried to use less energy? Let's say you have only a little success. Instead of the demand for oil increasing an additional 1% each day on top of the 10%, it only increases an additional 0.5%. Calculate the amount of oil needed on each of the 15 days and plot this data on your graph. Did conserving make a big difference or a little difference in the amount of oil used? With exponential growth, even very small changes result in big differences over time.