### Comprehension

* *
This module is a continuation
of the grain supply module.

**Questions**

- What trends did
you observe in the world grain supply?

- What trends did
you observe in demand for grain?

- How did world population
effect demand for grain?

- Per capita grain
supply means supply per person. How might the percapita supply
be impacted in each of these circumstance:
- increasing supply,
increasing population?
- increasing supply,
decreasing population?
- decreasing supply,
increasing population?
- decreasing supply,
decreasing population?

- What information
would you need to determine the per capita grain supply?

- What
kind of functions might be used to describe per capita grain
supply?

**Acquisition**

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

**Information/Assumptions
**

In this module we derive a function to describe the per capita
grain supply. If you did not complete the previous sections, click
here for functions describing
world grain supply and world population.

**Objectives To Determine**:

- per capita grain
supply
- whether per capita
supply increases or decreases.

**Application**

Retrieve the function S(t) you derived previously. Also, retrieve
a function P(t) describing world population. If you have completed
the population module, use that function.You may complete the
world population module at this
time or you may retrieve the function
we have derived. We will use these functions to predict how much
grain will actually be available **per person**. Here S(t)
is the world grain supply (in billion kilograms) and P(t) is the
world population, also in billions for t years from the year 2000.

**Assumptions**

- The current trend
for population continues.
- The current trend
for grain supply continues.

**Questions**

Use the functions S(t)
and P(t) to construct a function to describe the per capita grain
supply in year t. What are the units? Graph the function from
now through 1980 to 2075.

Estimate the per capita
grain supply for 2000 and for 2040. Identify the corresponding
points on the graph.

Predict when the per
capita grain supply will be 500 kilograms and label the corresponding
points on the graph.

Determine the rate
of change of the per capita grain supply for the indicated years.
(Note: you may want to use the "differentiation" capability
on the Math Pad to assist here). Discuss the significance of the
sign for each. a) 2000 b) 2045 d) 2060

Is the per capita grain
supply increasing at a faster rate in 2000 or in 2020? Explain
your answer in terms of the graph of the function as well as numerically.

Use the derivative
to decide when the per capita grain supply is increasing and when
it is decreasing.

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

Do you think that the
functions used are appropriate? If not, what might be better?

Compare your answers
in this section to your answers in the grain supply section. What
similarities are there? what differences? How could you explain
the differences.

Do you think that the
solution is reasonable? Why?

Do you think that the
per capita supply 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?

Would it be appropriate
to construct an alternative model?