The problem statement from S. Heinz "Mathematical modeling" goes as follows
I have a problem understanding what the statement of the problem means. In particular, "Use the data to graph $T$ and $CO_{2}$ as functions of $t$". Am I supposed to just graph the data points? Or use a Lagrangian interpolation? The only technique of modelling data that has been introduced is that of linear models and the polynomial models using the Lagrangian interpolation.
In the $CO_{2}$ figure when the question asks to graph a linear function which approximates the $CO_{2}$ data does this mean a polynomial of first order or should I just choose an arbitrary linear function?
Edit: I am allowed to use Mathematica or Maple.
In the first case it is not said how good the approximation has to be, or by what measure its quality is determined. You could just draw any line that goes through the middle of the point cloud, or you could do linear regression.
In the second case you are asked to find two lines where one is above the point cloud and one below, every point of the data between them, both somewhat parallel and as close together as possible. There might be different combinations of sides of the convex hull of the data cloud that fit that description. Then from those two lines compute the arithmetic average, which is a line that goes through the point cloud and thus approximates it in the first sense. To call it "best model" again assumes a measure of quality that is not provided or alluded to (at least not in that snippet).