Modelling Task

In my math class we are doing are doing a modeling task where we have to find a quadratic, cubic and other polynomial model for a given data set.
The table below is for a fishing rod with eight guides plus a guide at the tip of the rod.
guide # from tip- 1 2 3 4 5 6 7 8
distance from tip (cm)- 10 23 38 55 74 96 120 149
and the total length of the fishing rod in 230 cm.

So far all the polynomial models create an upward curve, do you have any ideas for any better functions that could model this data?
Since the distance from the tip cannot be more than 230 cm, would that make the polynomial models wrong because they go higher than 230 cm?

Quote:

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Originally Posted by alyssa92

In my math class we are doing are doing a modeling task where we have to find a quadratic, cubic and other polynomial model for a given data set.
The table below is for a fishing rod with eight guides plus a guide at the tip of the rod.

Code:

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guide #  | distance
from tip | from tip
---------+---------
  1    |    10
  2    |    23
  3    |    38
  4    |    55
  5    |    74
  6    |    96
  7    |  120
  8    |  149
---------+---------

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and the total length of the fishing rod in 230 cm.

So far all the polynomial models create an upward curve, do you have any ideas for any better functions that could model this data?
Since the distance from the tip cannot be more than 230 cm, would that make the polynomial models wrong because they go higher than 230 cm?

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The polynomials and the practical application are two differerent things! For instance, a polynomial is defined for all possible x-values, while your practical application cannot have negative inputs. (You can't have a negative length.) So the model "going higher than 230" is fine.

I'm not sure what you mean by an upward curve being a bad model...? Since the values (the distances) go up as the guide-numbers go up, wouldn't the curve have to be increasing...?

By the way, what is being modelled? I think you're being asked to estimate the number of guides necessary for a given length of pole, but I'm not sure. Kindly please reply with clarification. Thank you! :D

the details of the portfolio are as follows:

A fishing guide requires guides for the line so that it does not tangle and so thta the line casts easily and efficiently. In this task, you will develop a mathematical model for the placement of the line guides on a fishing rod.

the guide numbers and their distances were given in the earlier post...the overall length of the fishing rod is 230 cm and there are 8 guides from the tip.

and now we have to...

- define suitable variables and discuss their limits.
- find a quadratic function and a cubic function for the data points.
- find a polynomial funciton that passes through every data point.
- find another function that fits the data.
- use the quadratic model to determine where you could place a ninth guide. discuss the implications of adding the ninth guide.

i'm really stuck on the last question...i don't know what it means by 'implications of adding the ninth guide'. it would be a massive help if someone could give hints?? thank you so much...

Quote:

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I'm not sure what you mean by an upward curve being a bad model...? Since the values (the distances) go up as the guide-numbers go up, wouldn't the curve have to be increasing...?

By the way, what is being modelled? I think you're being asked to estimate the number of guides necessary for a given length of pole, but I'm not sure. Kindly please reply with clarification. Thank you! :D

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Thanks for the reply :)
Sorry, I worded the upward curve question badly, I was referring to it going over 230 cm...

But yes, later in the task we are given another set of similar data and are meant to compare it to our model. We are modeling guide number to distance from tip on a fishing rod. I was wondering if maybe a linear model could be good, because that would be more general and would work for other models? I did a polynomial to the 7th degree and it was weird. So far the best ive made is cubic because it had the smallest percentage error.

Hope this helped!

Hi, I know this topic hasn't been talked on in a while but I was wondering if someone could help me out with finding the quadratic cubic and polynomial functions of this data by using matrices. If someone could please respond within the next couple days. My assignment needs to be finished for the 3rd of January.

Quote:

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Originally Posted by curtis1919

Hi, I know this topic hasn't been talked on in a while but I was wondering if someone could help me out with finding the quadratic cubic and polynomial functions of this data by using matrices. If someone could please respond within the next couple days. My assignment needs to be finished for the 3rd of January.

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Sorry, but it's not MHF policy to knowingly provide help with questions that count towards a students final grade.

Thread closed.