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: 
     Study for the Free Response Section of the Final Exam.

Click here to go to the next page