Question

.

Answer 1

hi swaggba

Answer 2

hi

Answer 3

Are you still on these questions? xD

Answer 4

xd

Answer 5

There's really nothing to figure out. Just plug in the numbers into the function and see what you get.

Answer 6

Yes. This project is literally a walkthrough.

Answer 7

Okay.

Answer 8

Choose an initial value that is between 0 and 4 and is not a whole number. If I were you, I would choose 1/2 (lazy).

Answer 9

Then apply \(f\) ten times to it.

Answer 10

\[f\left(\frac12\right)=4\frac12-\frac1{2^2}=2-\frac14=\frac74\\
f\left(\frac74\right)=4\frac74-\frac{7^2}{4^2}=7-\frac{49}{16}=\frac{63}{16}\]
Do this eight more times.

Answer 11

It's literally the same thing, except starting with\[\frac{51}{100}.\]

Answer 12

Are you by any chance required to use software to solve these?

Answer 13

I don't want to do this by hand because I am lazy AF. Give me a second to write a computer program to do it for me.

Answer 14

I got these numbers using 0.5:

1.75, 3.9375, 0.24609375, 0.923812866210938, 2.84182125306688, 3.2913369778849, 2.33244880954708, 3.88947778903073, 0.429873684759558, 1.53470335418947

Answer 15

I got these numbers using 0.5 + 0.01:

1.7799, 3.95155599, 0.19142921789512, 0.729071726116543, 2.38474132264362, 3.85197411465044, 0.570191878664714, 1.95564873616366, 3.99803296539612, 0.00786426919039052

Answer 16

So, as you can see, the values differ tremendously as the iterations increase, which implies that the system is chaotic.

Answer 17

Those are the answers to 9, 10, and 11.