The iterates of population function

For r = 2 the population function (1) becomes

(2)

which we have already studied in Lesson 1. We see in table 1 that the initial population x0 = 0.3 gets iterated to final state x = 0.5 only after four iterations. Instead of the detailed worksheet of table 1, it is simpler to summarize in table 2 the successive iterates beginning from initial x0 = 0.3 to the fourth iterate x4 = 0.5.

Table 1. Iteration of function (2)

 

Table 2. Iteration values for r = 2

x0

x1

x2

x3

x4

0.3

0.42

0.4872

0.49967

0.49999

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