Badges: 17
Report Thread starter 11 years ago
I need an algebraic question for this table of values, if you can tell me how you got it, thanks. I know that the equation does not have constant first differences, which mean there should be an exponent in the equation but that's about it.
Number of Years Since 2000 (t) | Population in Millions (p)
1 31.1
6 32.2
11 33.4
16 34.4
21 35.4
26 36.2
Badges: 13
Report 11 years ago
Without having actually calculated anything, population (growth) questions should normally be approached using an exponential equation, not a polynomial. So if your question does not explicitly ask for a polynomial, try using  f(x)=ae^{cx} .
Badges: 16
Report 11 years ago
I suppose the two main approaches would be

i) To interpolate the data to a smooth curve (As you have 6 points, a 6th degree polynomial would be the simplest way to do that)
ii) To perform a statistical analysis and try and fit the data to a statistical model. As it would be expected due to the context (and the fact that looking at the data suggests that the growth in population is exponential) trying an exponential model seems the best way forward.

With point i) all you get is a smooth curve that passes exactly through the points but the data outside the range you know is useless.

With point ii) you should be able to get a smooth curve that passes pretty closely through the points (close enough for practical purposes) but then you also have a load of statistical techniques (statistical inference) that can be used to give an useable guide to what you can expect for values outside of your sample and and way to assign preference to which curves give a 'better' indication of what is likely to happen outside your sample (based on assumptions you have to make e.g. that the sample is representative of the whole etc. etc.)

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