**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