This module is a continuation
of the grain supply module. We will construct a function describing
the demand for grain and determine the break-even point.

**Comprehension**

**Questions:**

- What does "demand"
mean?
- What do you think
happens when supply is greater than demand?
- What do you think
happens when demand is greater than supply?
- Do you think that
demand for grain is increasing or decreasing?
- What factors do
you think affect the demand for grain?
- What effect does
increased population have on demand for grain?
- How do you think
mathematics can be used to study grain demand?

**Acquisition**
**Mathematical Information**: For a brief review of each concept,
click on the appropriate link.

**Information/Assumptions****
** Some of the factors you might have mentioned that
influence the demand for grain are population and the amount of
grain used per person.We make the following assumptions.

- The current trend
in world population increase continues. We provide you with
two possible models for world population, one linear and the
other exponential. Click
here for both.
- The current trend
in world grain supply continues. If you completed the grain
supply module, use the function you derived there. If you did
not complete that module, click
here for the function
- each person uses
188 kilograms of grain each year (this is based on current averages);
- per-person grain
requirements remain the same.

**Objectives To Determine**:

- worldwide demand
for grain, and
- when demand will
equal supply.

Application:
Apply mathematical topics and Tool Chest Applets to analyze world
demand for grain. Use the assumptions above.

**Questions**

- Write a function
describing the total demand for grain using the assumptions
above. Call the function D(t) where t = 0 in 2000. Clearly state
your units.
- Graph the demand
and supply functions on the same coordinate system (use the
plot-solve applet).
- Determine the point
of intersection on the graph. Give a verbal interpretation of
that point.
- Determine the year
when demand will surpass supply.

**Reflection**:
Assessing the method, solution and implications.

- Use the other population
function to write a new demand function. Which model do you
think is more accurate?
- Use your new demand
function to determine the year when demand surpasses supply.
- Do you think that
the demand function is accurate? Do you think that it is reasonable
to assume that this trend will continue? If not, what do you
think might happen?
- Do you think that
the solution is reasonable? Why?
- Would it be appropriate
to construct an alternative model?