IA Type II -- Population Trends in China

[nametaken]

What is the average time in order to complete this IA?

10 days maybe.

[dessskris]

by right you MUST finish a math IA within 10 days. but you know, some schools still give chances of first drafts and more than 10 days to do the IA. if your school is one of them, don't publish it on the internet! lol

but I personally think it 10x24 hours is enough. but obviously you wouldn't be working 24 hours a day and there are other things to do so I think if you spend 3 hours on this per day, 2 weeks should be enough...

it takes A LOT of time to figure out what the task exactly wants you to do. once you know everything then you can finish it in only 10 hours. or even less.

Edited July 1, 2011 by Desy Glau

[Markee]

by right you MUST finish a math IA within 10 days. but you know, some schools still give chances of first drafts and more than 10 days to do the IA. if your school is one of them, don't publish it on the internet! lol

but I personally think it 10x24 hours is enough. but obviously you wouldn't be working 24 hours a day and there are other things to do so I think if you spend 3 hours on this per day, 2 weeks should be enough...

it takes A LOT of time to figure out what the task exactly wants you to do. once you know everything then you can finish it in only 10 hours. or even less.

Hmmm... Quite a useful insight. Erm, Do you think this thread -by now- has every thing I would need in order to finish this IA within a week before the first draft deadline? Meaning to say, I would have already skipped the drafts and gone straight to the "real deal".

[dessskris]

Hmmm... Quite a useful insight. Erm, Do you think this thread -by now- has every thing I would need in order to finish this IA within a week before the first draft deadline? Meaning to say, I would have already skipped the drafts and gone straight to the "real deal".

Hmmm it's always good to have a draft before the final essay but it's all up to you.

Hmmm, although I haven't read the first few pages of this thread, I think this thread covers all the basic information needed in the task. but for some parts you still need to think a bit harder or do some further research because we can't (and didn't) tell you the answers

With everything in this thread as a guidance, I'll be sure I can finish the IA in 10 days (3 hours per day!) after doing just some more research and deep thinking.

[Markee]

Hmmm... Quite a useful insight. Erm, Do you think this thread -by now- has every thing I would need in order to finish this IA within a week before the first draft deadline? Meaning to say, I would have already skipped the drafts and gone straight to the "real deal".

Hmmm it's always good to have a draft before the final essay but it's all up to you.

Hmmm, although I haven't read the first few pages of this thread, I think this thread covers all the basic information needed in the task. but for some parts you still need to think a bit harder or do some further research because we can't (and didn't) tell you the answers

With everything in this thread as a guidance, I'll be sure I can finish the IA in 10 days (3 hours per day!) after doing just some more research and deep thinking.

Ok. Got it.

Thanks, Desy. As always, you are a big help in terms of Math. Oh by the way, is this easier or a bit more difficult than the "geometric sequences" IA that I did previously, if you can still recall.

[dessskris]

you're welcome! everybody has their own strengths and weaknesses

hmmm it depends on what method you choose to use I think the infinite summation IA is longer and more time-taking than this because you need to do a lot of repeats for various values of x and a in that task but this population trends IA is more straightforward I think but it might not be as simple as you think it would be. but I think this one is generally slightly more difficult. it's very subjective though, so I can't tell

[Markee]

heh heh... Yes indeed.

I see... Well, I won't know unless I start. I shall notify you again if I see if this thread doesn't have what I am looking for. But for now, thanks!

[Markee]

Based on my knowledge of population growth it will probably not be a linear model. An exponential graph might be useful, or maybe a modification of a logarithmic curve... the best hint I can give you is that if you plot it in excel, and select a trendline, then you can actually test out several types of models - linear, polynomial (from 2nd to 6th order), logarithmic, and probably something else I'm forgetting. I found this to be an invaluable tool!

Where is this so called "trendlines" located on MS Excel?

[dessskris]

plot a scatter graph first, then look for menu Format, Add Trendline, right click at the trendline, Format Trendline, choose the regression type.

[dessskris]

Outline for Population Trends in China IA

• Introduction
  
• Show a table of the China population
  
• Define your variables
  
• Plot a graph of the data from the table showing only the data points
  
• Comment on the trends observable from the graph
  
• Mention the function(s) that can possibly be modelled, explain why
  
• Create one model function algebraically
  
• Show all your working and calculation
  
• Consider limitations when serving your model function
  
• Plot your function together with the data points (on the same diagram)
  
• Comment on how well it fits. If it doesn't fit perfectly, revise your model.
  
• Use your GDC to generate the best fit logistic function, don't forget to show the equation
  
• Mention the values of K, L and M according to the model from your GDC. Interpret what they are in the population context.
  
• Consider limitations when serving your model function
  
• Discuss what will happen to the China population in the future according to your two model functions
  
• Show the other table of the data from IMF
  
• Comment on how well your two model functions fit the new data
  
• Pick one of the functions that you modelled that fits better. Modify this "old" function so that it fits the new data.
  
• Consider limitations when serving your model function
  
• Comment on how well this "new" function fits the data
  
• Conclusion

Edited July 4, 2011 by Desy Glau

[M1AguRstKin0B]

I think the variables here would be year and population in millions. Parameters might include greater than or equal to and less than or equal to signs. I'm guessing this question is there, right before the point where you graph it, to help you limit the axis to go from say 500 million to 1250 million, to make it a visible graph (it would be silly to have the years from 0 to 2000 for example). This is just a raw guess thought.. either way, the brunt of the portfolio seems to lie in the actual modelling. I would not spend too much time working on this particular part.

Hey Aron!

Could I ask you about the "Parameters" and "Variables" for this IA?

Erm, basically, I understand we should define them in terms of Population in general like factors affecting their growth such as the Year of which that number of population has increased e.g Economy boost. - Is my understanding correct?

As for "Parameters" it's all about the limitation, right? But, is it talking about in terms the graph of the population itself?

And do you also refer to the graphs as well in terms of the variables and parameters?

Thank you! (:

-If any one can answer this, Please do!-

[M1AguRstKin0B]

Outline for Population Trends in China IA

• Introduction
  
• Show a table of the China population
  
• Define your variables
  
• Plot a graph of the data from the table showing only the data points
  
• Comment on the trends observable from the graph
  
• Mention the function(s) that can possibly be modelled, explain why
  
• Create one model function algebraically
  
• Plot your function together with the data points (on the same diagram)
  
• Comment on how well it fits. If it doesn't fit perfectly, revise your model.
  
• Use your GDC to generate the best fit logistic function, don't forget to show the equation
  
• Mention the values of K, L and M according to the model from your GDC. Interpret what they are in the population context.
  
• Discuss what will happen to the China population in the future according to your two model functions
  
• Show the other table of the data from IMF
  
• Comment on how well your two model functions fit the new data
  
• Pick one of the functions that you modelled that fits better. Modify this "old" function so that it fits the new data.
  
• Comment on how well this "new" function fits the data
  
• Conclusion

THANK YOU DESY!

Would it be ok if I could ask you the type of models I could use?

Is there by any chance a compilation of ALL the Questions with their answers on this thread?

Edited July 4, 2011 by Corporal Cuhzee

[dessskris]

you are welcome.

would it be ok if I could ask you to read this whole thread first? or at least the first half... there have been a lot of discussions which you might want to consider in choosing the type of function that you want to model. if you then still have difficulty in choosing the function, ask again, telling me the functions that you have considered.

as for the previous question,

remember this is a math IA not a geography IA... the examiners don't care what actually affects the population (why it increases) and how, so you don't need to go that far.

in my understanding, for the variable it's like

let x be time in year, let y be the China population. something like that.

for the parameters, I'm not sure...

[M1AguRstKin0B]

you are welcome.

would it be ok if I could ask you to read this whole thread first? or at least the first half... there have been a lot of discussions which you might want to consider in choosing the type of function that you want to model. if you then still have difficulty in choosing the function, ask again, telling me the functions that you have considered.

as for the previous question,

remember this is a math IA not a geography IA... the examiners don't care what actually affects the population (why it increases) and how, so you don't need to go that far.

in my understanding, for the variable it's like

let x be time in year, let y be the China population. something like that.

for the parameters, I'm not sure...

Yeah sure. I've tried before but, sometimes it gets annoying once you keep seeing repetitions of the questions and answers more than 3 times.

Well, so far I've seen Matrices, I've heard about the six polynomials thing? and Logarithmic Functions?

Ohh, so it is ok to mention those, but not in much details?

Then, in terms of Variables and Parameters, I will keep referring back to the graphs?

[dessskris]

I find it annoying too to keep re-answering the same questions over and over again. hence why I don't really wanna do it again now.

but anyway.

yes, I suggest modelling a 6th polynomial, especially if you've learned matrices.

if you haven't, may want to go for another function (exponential/logarithmic, can't remember which one).

IMO you only need to talk about those when interpreting K, L, M. interpret them in terms of population.

don't get your last question. what do you mean?

[M1AguRstKin0B]

yeah. that's why there should be t his automatic program wherein it deletes all repeated questions and just compiles them in one place.

Ok. Only during KLM I will mention those things then... But for now, I would like us to focus on the first bits of this IA. Would it be ok as well if you could guide me step by step?

Well, I haven't done matrices thus far, only Logarithms.

uhm, basically, when I will be mentioning the Variables and Parameters, is it in terms of the graphs?

[dessskris]

to be honest I thought this post has already given a clear step by step guidance?

I still don't get your last question. variables and parameters are surely related to graphs, but variables do exist even if you don't have graphs. don't base your variables on the graphs, but do the opposite. I don't really know what parameters mean here but if my definition of it is correct, it should depend on the type of function that you want to model.

[M1AguRstKin0B]

ohhh, ok. But I mean like, what we are doing right now. Well probably after I get my head around this. Because my main problem right now will be the model that I will be using. Because I understand the first bit where it says variables and parameters. Thanks to you.

But basically, what I need major help in is the Apparent Trends, Types of functions could model the behaviour of the graph and Analytically develop one model function.

Edited July 4, 2011 by Corporal Cuhzee

[dessskris]

if you see my outline, what I actually did is just "re-writing" the task in simpler words that are easier to understand than those ambiguous words.

Apparent trends --> Comment on the trends observable from the graph

Types of functions could model the behaviour of the graph --> Mention the function(s) that can possibly be modelled

Analytically develop one model function --> Create one model function algebraically

If still not clear please ask again

[M1AguRstKin0B]

Yay~

Uhm, is it possible to ask the types of mathematical functions than can be used as models?