
Concept explainers
Cobweb plots (ExH). Here we visualize the simplified version of the Verhuist equation as we’ve seen in Mindscapes 24 and 25. That is, we consider the equation
We can visualize this repeated process on the graph of our sad parabola by first drawing in the diagonal line,
Notice how different the paths look! The Heart of Mathematics Web site contains a program that allows you to see this repeated process for any starting value of x.
These paths are called cobweb plots. The cobweb plot records the results of a repeatedly applied transformation-namely, taking a value for x, applying the formula to find y, then taking that result as the next x and again applying the formula to find the next y, and so on.
Now consider the graph of

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The Heart of Mathematics: An Invitation to Effective Thinking
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