This module is a continuation of the grain supply module.


  1. What trends did you observe in the world grain supply?
  2. What trends did you observe in demand for grain?
  3. How did world population effect demand for grain?
  4. Per capita grain supply means supply per person. How might the percapita supply be impacted in each of these circumstance:
    1. increasing supply, increasing population?
    2. increasing supply, decreasing population?
    3. decreasing supply, increasing population?
    4. decreasing supply, decreasing population?
  5. What information would you need to determine the per capita grain supply?
  6. What kind of functions might be used to describe per capita grain supply?

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

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:

  1. per capita grain supply
  2. whether per capita supply increases or decreases.

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.


  1. The current trend for population continues.
  2. The current trend for grain supply continues.


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?