Mathematical+Reflections+p.+46

9-16-08 NP Big Understanding: Many real world situations can be modeled and predicted using mathematics. Essential Question: How can I model a non-linear relationship?


 * __Mathematical Reflections 3; Page 46__**

1. The two graphs from problems 3.1 and 3.2 have 2 main similarities. Both graphs are graphs that have points that do not go in a straight line, but can still be relatively connected by a graph model. This means that both graphs are nonlinear, and have nonlinear graph models. Both graphs also have some sort of curve. The graph that went downward in investigation 3.2 had a curve that pointed toward the origin point before curving downward, and the graph that went upwards in investigation 3.1 had a curve that pointed in the opposite direction, to the right of the graph and not left before angling up. This means that one graph was an example of exponential decay, and the other of an inverse relationship.
 * How are the Graph models for these two relationships similar?**

2. The two graphs are different as well. The data in problem 3.1’s graph model arced upwards, growing larger with every jump, while the other graph was exactly the opposite, angling down and growing smaller with every jump. The exponential decay shown in problem 3.2 is very different from the inverse relationship shown in problem 3.1, which is also to be mentioned. Another major difference was that in 3.1’s graph the graph model’s curve arced toward the origin point before going to run next to the x value. 3.2 contained a graph model where the curve was angled more to the right hand lower corner of the graph before going upwards.
 * How are the graph models for these two relationships different?**

3. You can tell a relationship is linear if there is a fixed rate of change, meaning the gaps between values are always the same, and not varying. If there is a change in x, there is a change in y, which is always the same.
 * How can you tell a relationship is linear without making a graph?**

4. We have studies several types of graph models through this unit so far. One is a linear graph model, which is used when all of the values head in a relatively straight direction, where the points may not have a fixed rate of change, but the gaps are not too different between points. We have found inverse graph models, where as the x gets larger the rate of change gets affected negatively or positively. There are exponential graph models, where the rate of change is being changed exponentially with every data point. We have discovered several nonlinear graph models, that are models for data that has a pattern, but that either has no name for it or we simply have not got to yet.
 * Describe the different kinds of graph models you have discovered in your work so far in this unit.**

There are many different types of graph models, each with similarities and differences. There are linear, which go straight, there are non linear, inverse, and exponential models, each with unique characteristics, and some similarities in between.
 * __Summary__**