In this module we are working with models of the form
Your TI-92 has a number of features for examining these kinds of models. The most important thing is beginning by defining the function f(p) as shown in the screen below.
You can find the equilibrium points for a model like this by using the TI-92 Solve procedure as shown in the screen below.
Notice the answer above is symbolic. You can also work with specific examples using particular values of the constants a and c as shown in the screen below.
You may want to look at the TI-92 help modules on Making Tables for Sequences and Graphing Sequences for help on making tables of values for sequences and making graphs of sequences defined in this way. It is best to set up the Y= screen as shown below.
The TI-92 can even make cobweb diagrams. Notice the menu option AXES (the F7 key) in the screen above. Press F7 to select this menu. You will see a screen like the screen below.
Use the cursor pad to select the WEB option for AXES.
Then press ENTER once. Next select the TRACE option for BUILD WEB as shown in the screen below.
Next press ENTER twice to set both these options.
For cobweb diagrams the x-axis and the y-axis should have the same range. For a logistic model with c = 1000 both axes should range from 0 to 1000 as shown in the WINDOW screen below.
Now press green-diamond GRAPH to see the screen below.
This graph shows the function f(p) and the diagonal line. Notice the two points where the function f(p) crosses the diagonal line. These points are the equilibrium points. To start the cobweb diagram press the F3 key. You should see the screen below.
The text in the lower part of the screen shows the current values of n, x, and y. These are the number iof the current term of the sequence and the x and y coordinates of the moving point as we draw the cobweb diagram. Each time you press the right side of the cursor pad one segment of the cobweb diagram will be drawn. You can see the results on the graph and numerically. The screen below shows the result after several segments have been drawn.
