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Modeling Scenario


Author(s): Robert Krueger

Keywords: population dynamics dairy farmers' markets growth cow

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Resource Image A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.


Researchers should cite this work as follows:

Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Key Scientific Process Skills
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Bloom's Cognitive Level


problem. He doesn’t make any money selling milk. Unfortunately, he barely breaks even after expenses with the average market value of 100 pounds (just under 12 gallons) of milk selling for around $15. It is hard to make a living under those dire circumstances.

To combat this, he has developed an exceptional breed of Holstein cattle. These cattle are sought after by large dairy farms who want superior stock without the work of raising the calves until they are “fresh” (recently given birth to a calf and ready to milk). About 90% of the 9 million dairy cows in the United States are Holsteins.

Tim currently has 100 cows (female cattle) evenly distributed in age and enough bulls (male cattle) to aid in calf production.

Based on experience and a little research, he has enough land, shelter, and equipment to hold up to a maximum of 600 cows plus the bulls necessary for the operation.

All other cattle can be sold for profit. Our goal is to model the growth of Tim’s cow population using differential equations. 

We begin with a series of questions in which a model would be appropriate to address issues. Here is first question, "What other information do you think is necessary for us to begin to model the herd?  Write down a few thoughts."

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Author(s): Robert Krueger



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