Compare the projections to actual data

In case you were wondering why I only took data from 1950-1980, it is because I want to now load data for 1950-2000 and see which of our projections (if any) predicts the actual population growth accurately.  Let's load the complete data now:

[Graphics:../Images/index_gr_56.gif]
[Graphics:../Images/index_gr_57.gif]
[Graphics:../Images/index_gr_58.gif]

[Graphics:../Images/index_gr_59.gif]

[Graphics:../Images/index_gr_60.gif]

Let's plot this new data along with our three different functions (linearFit, quadraticFit, and exponentialFit) together now.  Notice that I need to extend the domains on the functions to graph this (keeping the same colors I used above):

[Graphics:../Images/index_gr_61.gif]

[Graphics:../Images/index_gr_62.gif]

[Graphics:../Images/index_gr_63.gif]

[Graphics:../Images/index_gr_64.gif]

Notice that these three functions now begin to diverge from each other significantly.

Questions

Which of our functions looks to be the "best"?  Why?  Do you expect this to be true as even more data is collected for future years?  
Graph the three functions through the year 2050 and discuss what sort of difference it makes which of our functions you choose to use to model the population growth.
A longer baseline:  Notice that our data started in 1950.  What happens if we use data for a longer period of time?  Use the data below which includes data for every 10 years between 1900 and 2000 and compare it with our three functions.  Which is best?  Why?
[Graphics:../Images/index_gr_65.gif]
[Graphics:../Images/index_gr_66.gif]
Use the new data (populationData3) to fit new linear, quadratic, and exponential functions.  Discuss which of these three functions works best (and why).  
Compare the new functions to the more detailed data in populationData2 and discuss whether the new functions fit that data as well.
So, can the population really be modeled by an exponential function or not?  What other improtant observations can you make about curve-fitting and data from this exercise?


Converted by Mathematica      May 11, 2003