Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

Finding the relation

a         1             2            3            4            5
b         3             0.75       0.33       1.875      0.12

what is the quickest and fastest way of finding the rule between relations like this???

and this

m         1             2           3            4              5       
n         7.2         5.09        4.16       3.6           3.22

They are pretty simple in that they will be only be in the form

, but the book gives this profusely long trial error 'draw graphs and see if it is a straight line' approach. Thx

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Finding the relation

For the first one, it is obvious that

Plotting the graph of

against

will give you a perfect straight line.

The second one is not so obvious to me so I can’t say anything about it. However, if you suspect

, just plot the graph of

against

and see if you get a straight line.

Last edited by JaneFairfax (2007-06-26 06:33:56)

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Finding the relation

How is the first one obvious though? Is there a non-graphical way to do this? I think there probably is... we did something kinda similar in physics, but I can't get my mind around it.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Finding the relation

Well, it was obvious because I got the answer just by staring at it.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Finding the relation

If

, then

.

This means that

and

.

Therefore,

and so

.
Finding k is the tricky bit. a is easy because that's just y[sub]1[/sub].

In your second question, n = 7.2/√m.

---

Why did the vector cross the road?
It wanted to be normal.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Finding the relation

Hmm, i will have to mull over that...

In the meantime, I came up with this:

where

is the nth term in the first table I provided.

The proving is incomplete... but it kinda implies that

, so

It might work on the other table too... dunno, and it breaks down when you get into tricky relations

Can you please check / improve this thx:)

Last edited by Identity (2007-06-26 04:59:29)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Finding the relation

That's kind of what I was saying. I probably should have mentioned that I was defining y[sub]n[/sub] as the nth term.

Basically, if y is proportional to x^k, then [2nd term]÷[1st term] = 2^k, and you can work out k from that.

---

Why did the vector cross the road?
It wanted to be normal.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Finding the relation

Oh I see, thanks then