1. Collect copies of the 2002 A.P. Exam F/R to grade as part of a quiz.
2. Hand out Tips for Taking the A.P. Exam.
3. Review Growth and Decay
Exponential Growth and Decay has one defining characteristic (and this is important):
the rate of y's growth is directly proportional to y itself. In other words, the bigger y is, the bigger y grows; the smaller y is, the slower it decays.
Mathematically, something exhibiting exponential growth or decay satisfies the differential equation:
This is the formula for exponential growth. We have already used this when we computed compound interest continuously. Remember the formula was:
This is probably the easiest way to remember the formula since we have used it for compound interest. However, it may be easier for some of you to remember it if you call the constant N instead of C in the original formula. Why is is easier to remember? It sounds like Roseanne pronouncing "naked" - "nekkit."
4. Example of Growth and Decay (Half Life Problem):
The Easter bunny's Evil Twin is hiding eggs made of a radioactive substance Nb-05, which has a half-life of 35 days. If the danger eggs have a mass of 2,000 grams, and you don't find the one hiding under your bed, how long will it take that egg to decay to a "harmless" 50 grams?
Solution:
5. Problem:
Assume that the world population's interest in the new boy band, "Hunks o' Love," is growing at a rate proportional to the number of fans (this is not to be confused with the Elvis hit, Hunka Hunka Burnin' Love"). If the Hunks had 2,000 fans one year after they released their first album and 50,000 fans five years after their first album, how many fans did they have the moment the first album was released?
(Answer is 894.427 original fans.)