find the equation for

[dpt90]

ok i dont know how to do this and was wondering if anyone would educate me in this

 

i have formula to get the length(l) of fish in relationship to time elapsed(t) ( l=80*(1-0.96^t)). and those numbers below are what i got, and i got a series of Weight values for the fish at those lengths.

 

 

Length(cm)	Weight(g)	months
3.2	                    	1.00
10.1	            15	        3.31
25	           236	        9.18
32.6	           520	        12.82
35.4	           660	        14.31
43.8	          1250	        19.43
45.5	          1425	        20.60
55.7	          2590	        29.19

 

how do i get the formula to calculate the weight of the fish

 

i did a bit of reading and was wondering if i could use integration to do this.

Edited March 21, 2009 by dpt90

[the tree]

Informed guessing is a surprisingly reliable technique. Given that weight is density multiplied by volume, what type of relation do you think you'll have between weight and length?

Edited March 21, 2009 by the tree
Consecutive posts merged.

[UC]

Informed guessing is a surprisingly reliable technique. Given that weight is density multiplied by volume, what type of relation do you think you'll have between weight and length?

 

<nitpick mode>

 

*mass* is density multiplied by volume. Technically, newtons would be the SI equivalent of weight, not grams.

 

</nitpick mode>

[the tree]

pssssht, doesn't change the direction I was going in.

[dpt90]

could i possibly do this using a graph ?????

[the tree]

As in plotting the data? Yeah, you could try. But the data set is pretty small so it'd be difficult to determine it's shape just by looking.

 

Think back to the question I asked - what kind of relationship do you expect it to be between the weight/mass and the length of the fish?

 

e.g. between volume and mass I'd suspect a linear relationship, between speed and breaking distance I'd suspect a quadratic relationship. etc. etc.

[dpt90]

i doubt it would be either of those 2 because there is another column wich i left out, the number of fish. As the months go on the number of fish decrease, and i need to find the best time to go fishing, that is the time that they grow most in......

[the tree]

I... forget it I'll just give the spoilers. Volume tends to increase with a cubic relation to scaling, if all the proportions stay the same. Which approximately speaking, they will. (or, close enough).

 

So the idea that I suggest you run with is that the weight of these fishes is proportional to the cube of their length.

 

i.e. [math]w=c\times l ^3[/math]. for some unknown coefficient [imath]c[/imath].

 

If you can find a reasonable estimate the value of that coefficient then you've formed a testable hypothesis.

 

To know when it's the right value (ish), you'll need to know the error that the formulae is producing. The relative error between a value [imath]x[/imath] and an approximation [imath]\bar{x}[/imath] is:

 

[math]\frac{|\bar{x}-x|}{|x|}[/math]

 

What you want to do is to find a value that minimises the relative error (or you could scrap the original idea and come up with a different equation entirely - provided that it can produce an equally low error whilst still making sense).

 

Now to find that coefficient, I'd say there's a number of different ways you could approach the problem.

 

(I'm imagining that this, like the last one, is really a computing problem so I've prepared the problem as I imagine it on a spreadsheet already take a look.)

 

1. Manual trial and error, complemented by basic common sense of course.
   
2. The brute force approach - MS Excel's Goal Seek should manage quite well.
   
3. If you're into that sort of thing, programming a more thought out numerical technique (such as interval bisection) - Excel provides you with the right enivorment to do this but you'll have to build the tools yourself.
   
4. Basic algebra to find the 'perfect' coefficient that matches one of the fish without error.
   • Doing this for a number of fishes and taking an average. This would work - but it would be cheating, really.

[dpt90]

oh cool thanx for the help again Tree, i wish i was as smart as you . i managed to get an average error of 1.9, but i think ill try the algebaic method you suggested.

[tjt]

I know this was a while ago but I'm currently stuck on the exact same question and am struggling to find a way to work it out was just wondering if you knew how you worked it out. As I can not wrap my head around it no matter what I read about it. 

[studiot]

2 hours ago, tjt said:

I know this was a while ago but I'm currently stuck on the exact same question and am struggling to find a way to work it out was just wondering if you knew how you worked it out. As I can not wrap my head around it no matter what I read about it. 

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