Back-To-School Night - A.P. Calculus 2

Welcome. Rather than give you all the boring rules and regulations of my class, how I grade, etc, let’s see what calculus is all about. Try this problem.

Wissahickon High has 1300 students. The 4 Honor Society officers, Matt, Leigh, Scott, Kathleen and 21 senior other members of Honor Society spread a rumor on day 0 that I am to become principal. A day later, 60 students know the rumor.

Question 1: How many days will it take the Question 2: When is the rumor spreading entire school to know the rumor? the fastest? a. 3 days a. day 1 b. 6 days b. day 4 c. 11 days c. day 7 d. 20 days d. day 10 Calculus deals with change. In A.P. calculus 2, we take what students learmed last year and apply it. One of the more interesting areas of change deals with what is called logistic growth. Rumors and logistic growth: A rumor spread as “tellers” pass it on to “hearers.” Once told, a hearer becomes a teller. The rumor spreads slowly at first when tellers are few. It spreads faster when both tellers and hearers are plentiful but slows down again as hearers become scarce and it stops when everyone knows the rumor. The number of people knowing the rumor (tellers) grows as shown.

tellers

time

00

We will now do an experiment that will simulate the concept of logistic growth: Let us suppose that one of you are sick. Suppose you transmit this illness to someone else in the room every day. We will now count off and demonstrate the growth of our illness using the TI calculator in which you have invested. The question you answered at the start of the class can be shown by the following graphs. The graph below shows the growth function of the rumor. Students will use calculus to find the equation of this graph. For those of you who are interested, its equation is:

Students =1300

1+ 51e!1300 .00069489( )t

As you can see, just about all students know the rumor at the end of 11 days. Answer is (c) The graph below shows the rate of growth of the rumor. At the start, the growth is not fast, the rumor grows faster as more students know it. But as many students know it, the growth slows down. At its peak, the rate of growth is about 290 students per days hearing the rumor on about day 4. The answer is (b).

My goal for the course is for students to learn new and complex mathematics, but more importantly, to enjoy and use what they learn. I hope you learned something tonight. Please call me if you want to discuss your child’s progress.