Mathematical+Reflections+p.+46+0910

9/9/09 CT Big Idea Many real world situations can be modeled and predicted using mathematics

Essential Question: How can I model a non-linear relationship?

Notes from Class (7/9/09): In Class we continued our partner-quiz test (if they weren't completed). We also did problem 3.2 (which we had to finish for homework). //Fancy economic word//- The law of diminishing returns : the more you get the less satisfied you are. example: the first bite you get out of a bag of chips is more tasty than when you have finished the last one left, once you eat the last one you want to have more so then you can have the same sensation over and over again.

. =Mathematical Reflections, 3.=
 * ==== In Problem 3.1, you investigated the relationship between the number of years and money invested in the bank account. ====
 * ==== In Problem 3.2, you investigated the relationship between the glass number and the amount of water in each glass. ====

==== The Graph in 3.2 has an inverse relationship so the points are starting at a high point and are decreasing along the way, unlike the graph in 3.1 where the points that are plotted start around 0 and increase in height along the way. 3.2 looks also more like an L and 3.1 half an arc. ====

**//3) How can you tell that a relationship is linear without making a graph?//**
==== Table: If you use a table, you can see that there is a linear relationship, because, every time x increases or decrease by the same number, y will increase or decrease by the same number each time. ====

Equation: If you use an equation, you can see if it is linear, because the equation will be set in this manner: y=mx+b
 * < x ||< y ||
 * < 1 ||< 2 ||
 * < 2 ||< 4 ||
 * < 4 ||< 6 ||

//**4) Describe the different kinds of graph models you have discovered in your work so far in this unit.**//

In this unit we have looked at inverse relationships in graphs and graphs with linear relationships (which can also have inverse relationships in them). We also looked at non-linear graphs.

SUMMARY: In this Investigation (3) we had to explain if the graphs we drew were linear or non-linear. we also had to find similarities and differences between the graphs and had to find answers to the problems given to us. in certain cases we were also asked to express our opinions in certain problems. ex. we were asked if thought it would be a good choice for chantal to keep her money until she was 18 or not.