Expert: Paul Klarreich - 9/16/2009

Question
Hello, I am doing what is known as a Math Portfolio from the IB Programme. If you go to http://occ.ibo.org/ibis/documents/dp/gr5/mathematics_sl/d_5_matsl_tsm_0801_1_e.p... and then go to page #12 that's pretty much what I have to do. I plotted a graph and then it asks what type of function models its behavior. First off, what do they mean by type of function? Do they mean whether it is linear, exponential, logarithmic, etc? And then, how do I know? Because the graph that I plotted looks to me linear, but at the beginning there is some sort of curve so I'm a bit confused. Can you please, if you can, plot the data in a graph and help me decide what type of fuction it is? Thank you. If there's anything else you would like to comment from that sheet that I have to do that can help me please do so. So that's pretty much it, thanks.

Answer
I found the document.  The graph (see attached, using Excel) looks like it might be a cubic polynomial.   It does not look linear except in portions, but that might be good enough.  I can't help you too much beyond that, but you might investigate something called 'CUBIC SPLINE' interpolation.