We try to structure and reproduce the world using different models. A mathematical model is one way of doing this. If we find that some things are interdependent, we can then find a rule describing this dependence and build a mathematical model.
When we move, we notice a clear relationship between the distance travelled and the time taken. This gives us a mathematical model for speed, v = s/t. That is, speed is the distance travelled divided by the time spent travelling.
In general, mathematical models are an approximation of the object under study and operates within certain limits.
Liisa-Petter studied a meteorite she found. She broke it in to pieces and measured the mass and volume of every piece and obtained the following results.
Lisa-Peter entered the results into a spreadsheet. The values seemed to line up almost in a straight line, so she fitted a line to them.
The slope of this line is approximately 3,2 and it describes the density. The mathematical model for density is mass divided by volume.
Mathematical models can also be exact . Like areas and volumes. Below are exact models of the areas of a parallelogram and trapezoid.
If the graph of a mathematical model is a straight line, it is called a linear model.
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