Question

Can somebody explain iterates to me. I still don't get them and would appreciate some help. I will give medals to best explanation. ( :

Answer 1

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Answer 2

Iteration in mathematics may refer to the process of iterating a function i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems. some examples are the Collatz conjecture and juggler sequences.

Answer 3

You may need to provide a specific example in order to obtain a particularly useful and directed response.

Answer 4

I can't seem to pull up the question. One moment.

Answer 5

Determine the first five iterates of f(x) = 1.2x(1 - x) for x0 = 0.1

Answer 6

if anyone can explain it to me.

Answer 7

\(x_{0}\) is a starting value.

Using this value in the function produces the next value in the seriess

\(x_{1} = f(x_{0}) = 1.2\cdot x_{0}\cdot (1-x_{0}) = 1.2\cdot (0.1)\cdot(1-0.1) = 0.108\)

Similarly,

\(x_{2} = f(x_{1}) = 1.2\cdot x_{1}\cdot (1-x_{1}) = 1.2\cdot (0.108)\cdot(1-0.108) = 0.0.1156032\)

Similarly,

\(x_{3} = f(x_{2}) = 1.2\cdot x_{2}\cdot (1-x_{2}) = 0.0.12268692\)

That all there is. Just keep using the new value to create the next.