ESSAY ONE: EXPLORATION WITH SOME SEQUENCES
1. x(n+1) = 3.2[x(n)][ 1 - x(n)]
Consider the behaviour of the sequence for various x(0). Use a spreadsheet to display a table and graph for a sufficient range of n.
In particular, investigate the behaviour of the sequence for x(0) in the range of
x(0) = .6875.
2. Investigate this sequence for a range of x(0).
x(n+1) = 3.83[x(n)][ 1 - x(n)]
3. For 0 < A < 2 examine x(n+1) = 1-A*x(n)^2 for -1 < x(0) < 1
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Supporting Documents: (Use these while reading the essay)
1. Matlab function codes for Investigations One and Two
2. Matlab function code for Investigation Three
3. GSP animation file for Investigation Three