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…

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…

Euler’s Method for Making Money

Chip Rollinson is a teacher at Buckingham Browne & Nichols School in Cambridge, Massachusetts. Today’s post is a note he sent to the AP Calculus Community bulletin board that I found interesting. I share it with you with his permission. I have done some minor editing. Chip wrote on February 5, 2015: I had an epiphany today…

A Family of Functions

Good Question 2, continued.  Today we continue looking at Good Question 2 from our last post. The jumping off place was the BC calculus exam question 5 from 2002. We looked at the differential equation  and its slope field and discussed the questions asked on the exam. Then we saw how to actually solve the equation…