Date: Tue, 22 Sep 2009 15:58:06 -0500 (CDT)
   From: Mark Jacobson <jacobson@cns.uni.edu>
     To: 810-025-01-fall@uni.edu
Subject: [810-025-01-FALL] Exponential Growth and Exponential Decay...

Hello 025 students,

Folding a sheet of paper in half 50 times exercise summary.

2 ^ 50
1125899906842624   sheets of paper you would have after doubling the
                    number of sheets 50 times, if you start with 1 sheet.
                    (Or fold one sheet of paper in half 50 times, if
                     it were possible!)

2 ^ 50 / 500
2251799813685.24800000000000000000  number of reams of paper,
                                     where a ream of paper has 500 sheets,
                                     which is the typical pack size.
2 ^ 50 / 500 *   2
4503599627370.49600000000000000000  2 inches is about the thickness
                                     of 500 sheets or one ream of paper,
                                     so this number is the inches thick
                                     the entire pile of sheets is.

4503599627370.49  /   (12 * 5280)   5,280 feet per mile * 12 inches/foot
71079539.57339788510101010101             is the divisor.

71,079,539.6 miles is a pretty good estimate for the height of the stack
              of paper.

Distance of the moon from the earth: 238,857 miles

"The average centre-to-centre distance from the Earth to the Moon is
  384,403 kilometres (238,857 mi), about thirty times
  the diameter of the Earth."

Distance of the sun from the earth: 92,580,000 miles

"The average distance from the Sun to the Earth is 1.496 x 1011metres (149
  million kilometres or 92.58 million miles)."

      92,580,000  miles from the earth to the sun
      71,079,540  miles for the paper's height

71,079,539.6 miles is a pretty good estimate
              for the height of the stack of paper.

We will use the Dictionary sometime in class to illustrate exponential 
decay concept and the binary search for a secret word in an unabridged
dictionary.

Mark