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IA Tidal Models

I really need help with my maths IA!

The aim is to investigate different functions that best model the heights of the tide from 12pm until 7pm.

1 (hrs after 12pm) --> 0.9 height (m)

2--> 1.8

3-->4

4-->6.9

5-->9.7

6-->11.6

7-->12.3

My maths teacher just gave us the IA sheet without telling us HOW we're suppose to approach it, so I have no idea how to do the questions..

The first 4 questions are:

Q1) Define all relevant parameters and variables clearly. Use technology to plot the data points from the above table onto a graph.

-> what are parameters?? does technology mean excel?

Q2) Comment on any apparent trends shown in the graph. What types of functions could you model the behavior of the graph? Explain your choices.

-> what does it mean by 'types of function'??

Q3) Analytically develop one model function that fits the data points on your graph.

Q4) On a new set of axes, plot your model and the original data. Comment on how well your model fits the original data.

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You may want to read the Population Trends in China IA thread btw, those questions are very similar with the ones asked there.

Parameters have been explained in that ^ thread.

Technology refers to the use of excel, graphing softwares and calculators.

Types of function: linear, quadratic, polynomial, power, exponential, logarithmic, etc...

Further questions are welcomed

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You may want to read the Population Trends in China IA thread btw, those questions are very similar with the ones asked there.

Parameters have been explained in that ^ thread.

Technology refers to the use of excel, graphing softwares and calculators.

Types of function: linear, quadratic, polynomial, power, exponential, logarithmic, etc...

Further questions are welcomed

I don't really get the 3rd question, what does it mean, "Analytically develop one model function that fits the data points on your graph."?

I'm not sure which year the assignment was actually meant for..

sorry i don't have a scanner so I can't scan and upload the sheet, but here are the rest of the qs on the sheet:

Q5) A researcher suggests that the height, h, of the tide at any time, t can be modeled by:

h (t) = asinb(x-c)+d

where a, b, c and d are parameters

Use technology to estimate a, b, c and d. Construct the researchers model using your estimates.

Q6) On a new set of axes plot the researchers model and the original data. Comment on how well this model fits the data.

Q7) Here are additional data collected the following year:

5 (hours after 12pm) --> 10.9 (height in m)

6--> 8.3

7--> 5.5

8-->3.1

9-->1.7

10-->1.8

Comment on how well each of the models above fits the new data.

Q8) Modify the model that best fits the new data. Comment on how well your modified model fits the new data.

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You are welcome I am glad to help

Analytically means algebraically or mathematically so you need to see the pattern in the graph and then do some calculations to get the expression of the graph.

I just graphed it and it looks like a part of a sine graph to me! But if I had to do this task, knowing qn 5 tells us that it's a sine graph, I wouldn't develop a sine model function in qn 3.

I would suggest plotting the graph in TI-Nspire if you have one, btw. I am using it and it can generate the best fit regression with 12 different regression types (and excel doesn't have some of them) so it can guide you to the answers to questions 2 and 3.

I hope you have some ideas on how to analytically get a function. Let me know if you don't, though, and I'll explain it to you.

Btw you are doing this as a practice, right? Not your real IA?

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how do you calculate and get the expression of the graph? i'm still stuck on that question..

no, i don't have TI-NSpire.. but i have an application called grapher.

and yeah this is just a practice IA.

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how do you calculate and get the expression of the graph? i'm still stuck on that question..

no, i don't have TI-NSpire.. but i have an application called grapher.

and yeah this is just a practice IA.

Ok great that it's just a practice so I don't mind giving excess help especially if it's your first time doing a Math IA

Try to graph that thing in your... Grapher? ok

My software suggested some equations that fit these data points but in questions 2 and 3 I personally would choose a cubic function. The general equation is y=ax3+bx2+cx+d right?

Since you have some data points, take 3 points, substitute their x and y values into that general equation and then solve for a, b and c

I would suggest choosing (1, 0.9), (4, 6.9) and (7, 12.3) btw

That is what I would do.. But if you want to develop a sine function directly in that part (even though I personally don't recommend this actually), then since you know that it's y=a*sin(bx-c)+d you can pick 4 points and substitute the values of x and y and solve for a, b, c and d (this might be harder though, thus highly not recommended). But you will get technology to find the equation in question 5 anyway so I'd really suggest finding that cubic expression.

Any doubt just come back here!