IA Type II -- Population Trends in China

[Sabs44]

actually, use your TI calculator. excel is ****ty for type 2 tasks. I use TI-Nspire, got a very nice interface, beautiful graphs and all so you may have a different view, but features-wise, TI is the best to use. it can generate the researcher's model and plot it with the data. too perfect.

I've used TI-Nspire as well and I agree with Desy about all the benefits of it. However, I would still say the GeoGebra is one of the best tools available, for this portfolio and most Math IA's!

[Steveo795]

Can anyone answer how to define parameters K, L, and M.

Is there an algebraic way to solve for each parameter?

[dessskris]

Can anyone answer how to define parameters K, L, and M.

Is there an algebraic way to solve for each parameter?

let me answer your second question first: yes there is, but it is very very complicated.

define K L M means: describe what those factors could be.

[PurpleVixen]

you can use regressions or matricies on your graphing calculator to figure those out

I'm not exactly clear how to "analytically" develop a model though, does that mean without technology?

[bomaha]

you can use regressions or matricies on your graphing calculator to figure those out

I'm not exactly clear how to "analytically" develop a model though, does that mean without technology?

You need to develop the model algebraically. Analytically means algebraically. Solve the equations you got from replacing "x" and "y" into your function simultaneously or by matrices.

[PurpleVixen]

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!

time can't be negative but years can, it can go behind zero like 50 BCE

[debbie8151995]

how can you prove that the function could be an exponential function? Is there a specific characteristic of exponential functions that the graph follows?

[Sabs44]

how can you prove that the function could be an exponential function? Is there a specific characteristic of exponential functions that the graph follows?

You don't have to prove that it's an exponential function (actually exponential isn't that good). But if you had your mind set on exponential, the first half of the data points come close to an exponential. I recommend looking at a polynomial... cubic or higher degree! Good luck!

[HoolaBaloola]

Desssyy!!!! I need your help! Ive tried doing a quartic function and all, double checked, done matrices and everything and its not looking like the graph its supposed to, it starts normal then it plummets up! and i get an equation that is totally wrong, what have i done wrong? Ive double checked EVERYTHING

[Sabs44]

Desssyy!!!! I need your help! Ive tried doing a quartic function and all, double checked, done matrices and everything and its not looking like the graph its supposed to, it starts normal then it plummets up! and i get an equation that is totally wrong, what have i done wrong? Ive double checked EVERYTHING

It's fine that it plummets down, but is it close to all of the data points before it plummets down? If so, then it's good! But if it plummets before the end of the data points something's wrong... did you change the years to (0, 5, 10...) or did you use (1950, 1955...)?

Edited December 9, 2011 by Sabs44

[HoolaBaloola]

Its horrible, its like really good for the first 3 data points, the it just skyrockets up! Ive changed the years into 0 5 10 and ive done inverse matrices and ive double checked them and i still get the same horrid equation

[HoolaBaloola]

I cant find any mistakes?! Yet the equation doesnt match the old curve? What have i done wrong? I used inverse matrices maybe thats wrong? I did the right order of multiplication and everything

[HoolaBaloola]

I used that guide posted to find the function using matrices, but I am not getting a equation anywhere near the data. The equation Excel gives me for a quartic function is y = 0.0001x4 - 1.1287x3 + 3356.2x2 - 4E+06x + 2E+09 the one I get when taking the RReF of a my own matrix is y = -0.001x^4 + 0.057533x^3 -0.747x^2 + 13.2617x + 554.8. What am I doing wrong in calculating this function I have switched the x values to increments of 5 starting at 0 and kept the y values the same my matrix looked like this

rref([[5^(4),5^(3),5^(2),5,54.2][15^(4),15^(3),15^(2),15,174.4][25^(4),25^(3),25^(2),25,373][35^(4),35^(3),35^(2),35,515.2]])

The values it gives me have the opposite signs of what excel gave me and when graphed the function is going down not up?

This is the last part of the assignment I have to do any help is appreciated.

I have almost the same problem as this guy!! except i didnt use rref instead inverse matrices

[HoolaBaloola]

MY equation is : y=-0.001x^4+0.00831x^3-1.1008x^2+14.452x+554.8

Which five* points did you use? Mine was different.

I used x=5, x=10, x=15, x=20

I used x=0 to find e which was 554.8

edit: of course for each x value i used the y-554.8 thing

i literally followed desy's guide bit by bit, i dont know what went wtong

Edited December 9, 2011 by HoolaBaloola

[ILM]

MY equation is : y=-0.001x^4+0.00831x^3-1.1008x^2+14.452x+554.8

Which five* points did you use? Mine was different.

I used x=5, x=10, x=15, x=20

I used x=0 to find e which was 554.8

edit: of course for each x value i used the y-554.8 thing

i literally followed desy's guide bit by bit, i dont know what went wtong

Nothing is wrong, if you are using a systematic approach, different points for sure will give you different answers.

[q1w2e3r4]

Um Hi, I'm having difficulties trying to understand what they mean by "trends" and how long it should be. It also says " what types of functions could model the behaviour" for this we can refer to our table right? and if we say, oh it might be qudratic, and prove it worng, is that all right?

[HoolaBaloola]

MY equation is : y=-0.001x^4+0.00831x^3-1.1008x^2+14.452x+554.8

Which five* points did you use? Mine was different.

I used x=5, x=10, x=15, x=20

I used x=0 to find e which was 554.8

edit: of course for each x value i used the y-554.8 thing

i literally followed desy's guide bit by bit, i dont know what went wtong

Nothing is wrong, if you are using a systematic approach, different points for sure will give you different answers.

That cant be right, everyone and his mother here has done this process right, there must have been something wrong, the guy mentioned 5 points? maybe i have to do a 5x4 matrix?

[ILM]

MY equation is : y=-0.001x^4+0.00831x^3-1.1008x^2+14.452x+554.8

Which five* points did you use? Mine was different.

I used x=5, x=10, x=15, x=20

I used x=0 to find e which was 554.8

edit: of course for each x value i used the y-554.8 thing

i literally followed desy's guide bit by bit, i dont know what went wtong

Nothing is wrong, if you are using a systematic approach, different points for sure will give you different answers.

That cant be right, everyone and his mother here has done this process right, there must have been something wrong, the guy mentioned 5 points? maybe i have to do a 5x4 matrix?

So you chose the following:

x=0

x=5

x=10

x=15

x=20

and you do create a five equations:

f(0), f(5),....etc

then you make up a matrices am i right and you solved it.

If this was your method, i don't think that there is a mistake.

[dessskris]

Desssyy!!!! I need your help! Ive tried doing a quartic function and all, double checked, done matrices and everything and its not looking like the graph its supposed to, it starts normal then it plummets up! and i get an equation that is totally wrong, what have i done wrong? Ive double checked EVERYTHING

you can message me your working and I'll point out your mistake.

or I can give you my email address? message me.

Um Hi, I'm having difficulties trying to understand what they mean by "trends" and how long it should be. It also says " what types of functions could model the behaviour" for this we can refer to our table right? and if we say, oh it might be qudratic, and prove it worng, is that all right?

trends like whether the graph increases/decreases, is there any maximum or minimum point, asymptotes etc

yes you may want to do that but it's useless :/ unless from there you can deduce what function could model it better.

[debbie8151995]

how can you prove that the function could be an exponential function? Is there a specific characteristic of exponential functions that the graph follows?

You don't have to prove that it's an exponential function (actually exponential isn't that good). But if you had your mind set on exponential, the first half of the data points come close to an exponential. I recommend looking at a polynomial... cubic or higher degree! Good luck!

Thanks! I now realize exponential's not the best. So, I'm using cubic for my model. When they say "analytically develop one model function", can we use regression to find the equation or do we have to use matrices? If its matrices, I'm screwed because I don't understand it