Activity Overview
Students explore several models representing the growth (or decline) of a biological population. They study models of a single population that have a closed-form solution, and models of several interacting populations that have an open-form, numerical solution.
Before the Activity
See the attached PDF file for detailed instructions for this activity
Print pages 57 - 68 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the activity procedures:
Exponential and Logistic Regression:
Fit exponential and logistic growth models to the U.S. Census population data for years 1790 to 1990
Enter the data as a stat list
Compute the regression coefficients
View the resulting exponential function and the original data on the same graph
Calculate a logistic regression and graph it
Note the exponential model is not close to the actual data, while the logistic model fits the data better
Find the expected population for the year 2020 using the logistic model
Logistic Growth Models and Critical Depensation:
Graph and compare the Logistic Growth and Critical Depensation differential equation models
Change the initial conditions to see how the critical depensation differential equation model differs
Predator-Prey Model:
Enter the system of differential equations for a predator-prey model
Plot the slope field function and trace several possible graphs for the solution to the differential equation
Competitive Species Model:
Enter the system differential equations that models two similar species living in the same habitat and competing for the same resources
Study the direction field
Note that there are several solutions to the equations that move towards a limit where one population wins
SIR Model:
Enter 3 differential equations
Graph the equations together
Study the direction field and explore various solutions
After the Activity
Students complete the problems on the exercise page.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary