Review Topics

 Home Grain Supply Calculus Supply versus Demand Per Capita Grain Supply

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:

1. What does "demand" mean?
2. What do you think happens when supply is greater than demand?
3. What do you think happens when demand is greater than supply?
4. Do you think that demand for grain is increasing or decreasing?
5. What factors do you think affect the demand for grain?
6. What effect does increased population have on demand for grain?
7. 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.

1. 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 for both.
2. 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 for the function
3. each person uses 188 kilograms of grain each year (this is based on current averages);
4. per-person grain requirements remain the same.

Objectives To Determine:

1. worldwide demand for grain, and
2. when demand will equal supply.

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

Questions

1. 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.
2. Graph the demand and supply functions on the same coordinate system (use the plot-solve applet).
3. Determine the point of intersection on the graph. Give a verbal interpretation of that point.
4. Determine the year when demand will surpass supply.

Reflection: Assessing the method, solution and implications.

1. Use the other population function to write a new demand function. Which model do you think is more accurate?
2. Use your new demand function to determine the year when demand surpasses supply.
3. 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?
4. Do you think that the solution is reasonable? Why?
5. Would it be appropriate to construct an alternative model?