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World Coal Supply

In this module we will study availability and world use of coal. In particular, we will determine the current usage rate and how long the coal supply will last at this rate of consumption.

Comprehension: Understanding the problem; visualizing a solution

  1. What is coal?
  2. What are some of the uses of coal?
  3. Do you benefit from coal? How?
  4. Which countries of the world do you think use coal?
  5. Do you think the Earth holds enough coal to supply its population forever? If not, how long do you think it might last?
  6. How could you answer this question, i.e., how could you study use and availability of coal?


Mathematical Topics: Learn or review mathematical concepts and skills needed to study coal availability (see Menu at the left of this screen

Information/ Assumptions

  1. The 1980 world coal supply is estimated to be 8.529 (x106) million tons.
  2. The rate of usage of coal in 1980 and 1995 was 2507.344 and 3096.010 million tons per year, respectively.
  3. Based on these two statistics, the rate has been increasing linearly since 1980.
  4. This rate of usage will continue.

Our ultimate goal will be to obtain an estimate for the number of years before the world runs out of coal. We will consider the estimated coal supply for the world, determine the present amount and its rate of usage. From this we can predict how long the coal supply will last. Specifically, our objectives are listed below (subject to the above assumptions).

Objectives To Determine:

  1. Current usage rate;
  2. Present world coal supply (in 2000);
  3. The amount of coal used in the future;
  4. The number of years before the world coal supply is exhausted.


Apply mathematical topics and Tool Chest Applets to analyze world coal supply


  1. As stated in Assumptions 3 and 4, we will assume that the increase in the rate of usage of coal is linear. Use Assumption 3 to get two points with coordinates t for year, t = 0 in 2000, and C(t) for rate of coal usage in year 2000 + t. Then determine the linear function C(t) which goes through these points. This function will be used to estimate the increasing rate in million tons of coal per year in 2000 + t. Since C(t) describes a rate of change, you will recognize it as a derivative.
  2. Use the function C(t) and the integral to determine the amount of coal used from 1980 through 2000.
  3. Now use Assumption 1 to find an estimate of the amount of coal available in the year 2000.
  4. Next, use the integral to find a function which gives the amount of coal that will be used from the year 2000 through an unspecified year 2000 + x.
    Our ultimate goal is to find out when the world’s coal supply will be exhausted—this date is the unknown x, i.e., in the year 2000 + x all the coal will be gone if the present usage rate continues.
  5. Use the function from #4 to determine the year when all the world’s coal will be used up.

Reflection: Assessing the method, solution and implications

  1. Do you think that the functions used are appropriate? If not, what might be better?
  2. Do you think that the solution is reasonable? Why?
  3. Do you think that the usage rate is accurate? Do you think that it is reasonable to assume that this rate will continue? If not, what do you think might happen?
  4. Would it be appropriate to construct an alternative model?