Question

@peachpi

Answer 1

It's difficult to explain without the visuals so yeah.

Answer 2

1. The function would be linear? Or cubic?

Answer 3

you were right. it's cubic

Answer 4

Okay good.

Answer 5

I'm not sure why some are positive while some are negative.

Answer 6

How is it cubic? Because linear just go's straight up and expo starts stable then swoops up.

Answer 7

because volume increases between some values and decreases between others. positive rate of change means the function is increasing, negative rates of change means it's decreasing

Answer 8

the rate of changes are just the volume of the cubes right?

Answer 9

okay that's cleared up.

Answer 10

no, the rates of change are the CHANGES in volume over the interval. So going from 1 cut to 2 increases volume by 28 cubic units. Going from 3 to 4 decreases volume by 44 units

Answer 11

oh oh okay right.

Answer 12

Okay confusion cleared.

Answer 13

you know it's cubic because volume is in cubic units for one.
tbh, this question is incredibly misleading. This is like the one we did where the equation turned out to be 2^x. You're building your data from a specific function, so you don't really need to do regression. That's what @mathmate was saying. When you do regression you're going to get the function you used to build the data

Answer 14

When you calculate volume, you're using
\[V=x(12-2x)(12-2x)\]
That's exactly what you'll get when you do regression

Answer 15

***12 - 2x***

Answer 16

so should I tell you the height of all of my cubes? Maybe that will also help me understand this better.

Answer 17

ok. If you use the spreadsheet to do regression, make sure you're using the right degree on the polynomial. It's cubic so it should be degree 3

Answer 18

The heights are 1, 2, 3, 4, and 5, right?

Answer 19

yep

Answer 20

thats what YOUR equation looks like sorry thats what I meant

Answer 21

mine looks like y= 4x^3 - 48x^2 + 144x - 1.123E-12

Answer 22

So the equation is 4x³ - 48x² + 144x because 1.123E-12 is very close to 0 and it can be dropped.
The r^2 = 1 means that that equation is an exact fit for the data, which makes sense b/c we used the equation to create the data. In general the closer r^2 is to 1, the better the fit.

Also 4x³ - 48x² + 144x is what you get if you multiply out x(12-2x)²

Answer 23

plug in 2.5 for x

Answer 24

into the equation we just got?

Answer 25

yes

Answer 26

because x is the change of volumes right?

Answer 27

x is the size of the cut
y is the volume
the rate of change is the change in volume

Answer 28

okay got it. so it's 122.5

Answer 29

yes

Answer 30

not sure if if I round up.

Answer 31

I wouldn't.

Answer 32

okay.

Answer 33

Well thank you again so much. I won't bother you again -ever lol. You're the best x100

Answer 34

haha its no bother. you're welcome