IA Type II -- Population Trends in China

[Karl H T]

Hi everyone!

Luckily, I have a few days more to finish my first Maths portfolio. My god how the time flies - it was a few days ago when we got the assignments and now I'm sitting behind a desk with a cup of coffee...

Anyways, back to my question:

We've been given data regarding population at a specific period of time. There is a specific point in the assignment that goes something like this:

A researcher suggests that the population, P at the time t can be modelled by P(t) = K / (1+Le^-Mt)


 where K, L, and M are parameters

It is my job to estimate and interpret K, L and M. I'm not quite the independent thinker in Maths and I'm stuck with this one. If anyone has tips how to approach this question - whether is it possible to rely on some computer program and a guided estimating process; or should I spare some paper and pencil for calculating?

Let me get another cup of coffee now...

Edited May 6, 2010 by Karl H T

[Saph]

Hey all,

A week ago I was given a Maths Portfolio to do, called "Population Trends in China". (It's attached)

I know how to generally solve and do the portfolio, however, I am stuck on one of the very first questions! Define all relevant variables and parameters clearly. I have no idea about what a parameter is. Now I have been looking up several definitions, asking friends, and I've found no answers that I really understood and could link to the first set of data provided. ):

The closest easy-to-understand definition I've found is: "These parameters include population size, birth and death rates, and the population growth rate." (http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0865427402.html)

- So that is what a parameter is concerning populations? Other definitions mention that it is a constant, but birth- and death rates usually aren't?

I sincerely hope somebody can help me a bit on the right track (and that I haven't broken any of the forum rules!).

!EDIT Feb 2011!: Please STOP private messaging me about how I did my IA! Scroll down and through the thread and you'll see LOTS of tips and good hints as to how to deal with this IA. The whole thread is drowning in good help! (:

Maths_SL_China_Population.pdf

[DustinChambers]

Hey all,

A week ago I was given a Maths Portfolio to do, called "Population Trends in China". (It's attached)

I know how to generally solve and do the portfolio, however, I am stuck on one of the very first questions! Define all relevant variables and parameters clearly. I have no idea about what a parameter is. Now I have been looking up several definitions, asking friends, and I've found no answers that I really understood and could link to the first set of data provided. ):

The closest easy-to-understand definition I've found is: "These parameters include population size, birth and death rates, and the population growth rate." (http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0865427402.html)

- So that is what a parameter is concerning populations? Other definitions mention that it is a constant, but birth- and death rates usually aren't?

I sincerely hope somebody can help me a bit on the right track (and that I haven't broken any of the forum rules!).

For this section simply describe factors that cause population to rise and to fall.

[isurvive]

Hey,

I was assigned the same one last Thursday and it's due this Friday and I haven't got anything done except the graphs.

So from what I understood in class, parameter is the limitation of something. It's like applying a negative number on the X-axis on the graph of trends in China, it is impossible because the years can't be negative. So this is one of the parameters. It's something like that!

[Daedalus]

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.

[gkong]

I hated this IA because we didn't learn statistics we had a lot of guessing to do.

Lots of technology involved! I'm not sure which topics you guys have covered, but for creating your own try using transformations.

[Dzeb]

isurvive and Aron are both right, define what both axis represent and define the limits of these axis. Also, you would probably want to explain your reasoning.

[Saph]

Thank you all so much for helping! This confirmed what I've written about now - brieftly nonetheless! o;

Hey,

I was assigned the same one last Thursday and it's due this Friday and I haven't got anything done except the graphs.

So from what I understood in class, parameter is the limitation of something. It's like applying a negative number on the X-axis on the graph of trends in China, it is impossible because the years can't be negative. So this is one of the parameters. It's something like that!

Firstly, you better start right now! Been working on this for 2 weeks now, and I'm soon finished.. Just a few more days.. Oh, wait mine is due to tomorrow. Ups, gotta do an allnighter =P

Secondly, I would say it is possible for the X(!) value to go below zero. For instance if you choose the x-axis to be from year 0 to year 2000. There were living people in China BC

I've used 2 programs which were both great, easy and applicable. Not sure though, if I'm allowed to recommend them, so I'll wait (:

Edit (because of sweetnsimple786's answer below): I used

Geogebra

MS Excel

GDC - regression (won't score many points on technology but will help giving ideas of L,K,M values)

--- More about these in post 55 and from me on page 4.

Edited February 23, 2011 by Saph

[sweetnsimple786]

Yes, you can recommend programs or software you used =)

We just don't want people to give answers or ask for answers without working something out on their own.

And while you could make the time negative, it's not really applicable for this kind of thing, and I don't know how much being cute/creative pays off for math IAs. =/

Good luck!

[little_master]

Hey All,

I am also having problems with the graphs, and meeting the points with it. I have tried doing a linear model, which did not work! Does anyone have any advice they could post!

It will be greatly appreciated!!

[Daedalus]

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!

[little_master]

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!

But how about cubic and quartic equation....do you have any ideas on them, and if they could possibly work??!

[Junkstuff]

Hello everyone,

In this portfolio the only confusing part is what K, L and M are meant to represent in the researchers model ive been trying to figure it out for a few days now but for some reason i keep getting mixed up with what effect they have on the line!

any advice?

Edited May 26, 2010 by Junkstuff

[sweetnsimple786]

This should help some: http://cerebro.xu.edu/math/math120/01f/logistic.pdf [the bold stuff haha]

Plugging numbers in usually helps as you keep the other two variables constant. K is the easiest. Making t infinitely large will show you what K is, which is explained on that site.

[Szoszana]

Hello to everybody!

I am nearly finished with this one, only wondering whether it is better to include graphs that show grids or ones that do not. Does that makes any difference whatsoever?

Edited June 23, 2010 by Szoszana

[sweetnsimple786]

I would go with your gridded graph. Sometimes, when you have grids, they make seeing the data points hard because there are too many lines. For your graph, though, there aren't many intervals on the y-axis, so it's clear where the points lie, and the grids help me to see the distance between the 500 or 1000 mark and any of the points.

The one without the grid would be fine, but your grid one looks nicer in this case.

[Zuza]

Yes, go with grids It looks better like this Btw I used the same program and it was very helpful. If you have any problems I can help, since I finnished that portfolio already. I must say that the use of technology was pretty hard, so if you need anything I'm willing to help Good luck

[JennyJoy]

Hello everyone!

First of all, I wish you wopnderful holidays - I believe that all of us DO really deserve a bit of laziness. )))

I wanted to ask, what kind of 'technology' did you use while estimating and interpreting parameters K, L, M? I've got an idea how to deal with it but it has virtually nothing to do with technology itself and I need some more data (from the Internet sources). Am I going in the right direction? Can anyone give me a hint? I'll be very grateful.

))) Thank you in advance.

[deissi]

Use some kind of an excel table with the data. It might seem very useless but it's using technology according to the IB. You could, say, have a table for values that the researcher's function yields in 2020, 2030 etc. The modelling software you use for the graphs is also technology. So is using your calculator.

[cherries94]

I am just wondering what type of graph did you do in the first part of it, as in linear/sin or whatever??

and also i thought parameters were like m=gradient and c=y-intercept or stuff like hat and the constraints arew x>0 and y>0 or something like this??

thanks