Quote of the Day:
"Truth is much too complicated to allow anything but
approximations." -- John von Neumann
Objectives:
The student will review for the A.P. Exam.
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.)
6. Assignment:
Read p. 603 - 604
p. 608 (5, 7, 9, 12, 17)
Winchester Population Problem
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