Question

***Will fan and medal***
What is the average common ratio between the successive height values of ball 1? Ball 2? Ball 3? Experimental errors may cause common ratios to have some variances within the data for one ball. Use the average common ratio.

Answer 1

http://assets.openstudy.com/updates/attachments/53a9f80de4b0ffdda15ed41b-xiphoidx-1403648031175-8.04.png

Answer 2

the table ^^

Answer 3

@Hero

Answer 4

Do you know how to find the common ratio in a geometric series?

Answer 5

no..

Answer 6

OK. In any series you have the starting spot, or 0th, spot, then the 1st comes after it, then the 2nd, and so on.

So in this:
1, 2, 4, 8...

1 is the 0th spot, 2 is the 1st spot, 4 id the 2nd spot, and so on.

These are normally shown using a sub script:

\(n_0, n_1, n_2, n_3...\)

For any spot, the following should be true in a gemetric serries:
\(\Large n_{i+1}=rn_i\)

Where:
\(\Large n_i\) is one spot.
\(\Large n_{i+1}\) is the next spot
\(\Large r\) is the common ratio between all spots.

Answer 7

so what numbers do i plug in??

Answer 8

In my example, I have 1, 2, 4, 8, 16, 32, and so on...

2=r1
4=r2
8=r4

I can use any of those to solve for r. I would find it was 2. So each space is twice the space before it. That is the basics of a geometric series.

Answer 9

Now, in your balls, you are given things like:
3, 2.4, 1.9, 1.5, and 1.2

That is ball 1.

Answer 10

What they said is "average common ratio" so you need to find the common ration for each change in height, then anverage them.

Answer 11

so the formula you gave me is how you find the common ratio?

Answer 12

Yes, it can find it for all spots in a real geometric series. However, your problem is saying this is just sort of a geometric series, so you end up finding it 4 times per ball and averaging it for each ball. Not all, but each, as in one average for each ball.

Answer 13

can you maybe set one up so i can see how??

Answer 14

Let me take my 1, 2, 4, 8 example and change it a bit to show what I mean. What if it was this:

1, 2.2, 3.9, 8

Well, now it is not a true geometric series. But I can find the average common ratio:

\(2.2=r_11\)
\(2.2/1=r_1\)
\(2.2=r_1\)

\(3.9=r_22.2\)
\(3.9/2.2=r_2\)
\(1.773\approx r_2\)

\(8=r_33.9\)
\(8/3.9=r_3\)
\(2.051\approx r_3\)

Now I average my three ratios:

(2.2+1.773+2.051)/3=2.008

As you can see, this is close to when I had a real geometric sequence with a ratio of 2. But it is not 100% the same.

Answer 15

thank you so much!!!

Answer 16

So you will do the same thing, for ball 1: find the 4 ratios, add them up, divide by 4. THen on to ball 2, etc.