The Logistic Equation

After my last post, I realized I have never written about the logistic growth model. This is a topic tested on the AP Calculus BC exam (and not on AB). Here is a brief outline of this topic. Logistic growth occurs in situations where the rate of change of a population, y, is proportional to…

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Logistic Growth – Real and Simulated

The logistic growth model describes situation where the growth of some population is proportional to the number present at any time and the difference between that amount and some limiting value called the “carrying capacity.” The standard example is this: a small group of rabbits is placed on an island. The population will grow rapidly…

Everyday Series

Our BC friends will soon be starting to teach series. Today, to emphasize that series are all around us, I would like to discuss series that we see every day: numbers. Long ago I was taught that no one has ever seen a “number.” Have you ever see a four? What we see are numerals, symbols or…

Density Functions

Density, as an application of integration, has snuck onto the exams. It is specifically not mentioned in the “ Curriculum Framework” chapter of the new Course and Exam Description. There is an example (#12 p. 58) in the AB sample exam question section of Course and Exam Description.The first time this topic appeared was in…