**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

- What is coal?
- What are some
of the uses of coal?
- Do you benefit
from coal? How?
- Which countries
of the world do you think use coal?

- Do you think the
Earth holds enough coal to supply its population forever?
If not, how long do you think it might last?

- How could you
answer this question, i.e., how could you study use and availability
of coal?

**Acquisition**

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

Information/ Assumptions

- The 1980 world
coal supply is estimated to be 8.529 (x106) million tons.

- The rate of usage
of coal in 1980 and 1995 was 2507.344 and 3096.010 million
tons per year, respectively.

- Based on these
two statistics, the rate has been increasing linearly since
1980.

- 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:**

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

**Application**

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

**Questions**

- 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.

- Use the function
C(t) and the integral to determine the amount of coal used
from 1980 through 2000.

- Now use Assumption
1 to find an estimate of the amount of coal available in the
year 2000.
- 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.
- 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

- Do you think that
the functions used are appropriate? If not, what might be
better?
- Do you think that
the solution is reasonable? Why?
- 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?
- Would it be appropriate
to construct an alternative model?