(*^

::[	frontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.1";
	macintoshStandardFontEncoding; 
	paletteColors = 128; automaticGrouping; currentKernel; 
	fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8,  24, "Times"; ;
	fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6,  18, "Times"; ;
	fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6,  14, "Times"; ;
	fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20,  18, "Times"; ;
	fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15,  14, "Times"; ;
	fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12,  12, "Times"; ;
	fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; ;
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	fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5,  12, "Courier"; ;
	fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; ;
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	fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287,  12, "Courier"; ;
	fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic,  10, "Geneva"; ;
	fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = leftheader, inactive, L2,  12, "Times"; ;
	fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7,  12, "Times"; ;
	fontset = leftfooter, inactive, L2,  12, "Times"; ;
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	fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
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	fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
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:[font = special1; inactive; preserveAspect; ]
                 Discrete Dynamical Systems and Difference Equations

The cell below contains the data for Question 6 in the Check Your Understanding part of this section.  Evaluate the cell now.
;[s]
3:0,2;68,0;173,1;196,-1;
3:1,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;1,13,9,Times,1,12,0,0,0;
:[font = input; preserveAspect; ]
Clear[Data6, Seq6]

Data6 := {12000, 13097, 14115, 15199, 16202,
          17242, 18292, 19364, 20431, 21498,
          22500, 23573, 24614, 25633, 26671,
          27743, 28805, 29849, 30878, 31880}
          
Seq6[n_] := Data6[[n]]          
          
:[font = special1; inactive; preserveAspect; ]
The cell below illustrates how Mathematica  can be used to analyze this kind of data.  Evaluate the cell now.
;[s]
5:0,0;31,1;42,0;87,2;109,0;110,-1;
3:3,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
TableForm[Table[{i, Seq6[i], N[Seq6[i]/Seq6[i - 1]]},
           {i, 2, 20}]]
:[font = special1; inactive; preserveAspect; ]
The cell below contains the data for Question 7 in the Check Your Understanding part of this section.
:[font = input; preserveAspect; ]
Clear[Data7, Seq7]

Data7 := {12000, 13455, 15124, 17134, 19455,
          21839, 24531, 27786, 31246, 35140,
          39682, 44805, 50365, 56934, 64849,
          72636, 81367, 91684, 103579, 118072}
          
Seq7[n_] := Data7[[n]]
:[font = special1; inactive; preserveAspect; ]
The cell below contains the data for Question 8 in the Check Your Understanding part of this section.
:[font = input; preserveAspect; ]
Clear[Data8, Seq8]

Data8 := {120.00, 118.54, 117.06, 115.68, 114.28,
          112.89, 111.58, 110.31, 109.05, 107.82,
          106.65, 105.54, 104.48, 103.40, 102.38,
          101.42, 100.45,  99.49,  98.57,  97.62}
          
Seq8[n_] := Data8[[n]]
^*)