3.7 Case Study: Population Modeling
By the time you complete the CSC, you should know:
ExamplesSuppose we want to model the growth of a bacteria colony. We know that the rate of change of the population (P) is directly proportional to the population. Early observations suggest that they are in fact equal. If the initial population is 100, use Euler's method with stepsize = 0.1 to predict the population in 6 hours.
After three hours, we observe the bacteria colony and find the population is now 1600. Use this information to solve the differential equation in the previous example, and find a more accurate constant of proportionality. How does this model differ from the previous one? Again, predict the population at t = 6 hours and compare with the previous estimate.
More research indicates that the growth of the bacteria colony is proportionally dependent on the amount of oxygen available. In the controlled environment where our sample resides, all the oxygen will be exhausted in 3 days (72 hours). Thus, our new differential equation modeling the bacteria growth is
AppletsEuler Population Predictions
VideosSee short videos of worked problems for this section.
ExercisesSee Exercises for 3.7 Case Study: Population Modeling (PDF).
Work online to solve the exercises for this section, or for any other section of the textbook.
Resources on the WebInformation on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
The Cambrian period was 540 to 500 million years before the present. Question: Was diversity (measured as number of invertebrate genera) in the Cambrian period logistic?
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel