Mathematical+Reflections+p.+59

//Sept. 21, 2008 AS Big Idea: Many real world situations can be modeled and predicted using mathematics. How can I explore patterns in the world? Notes from Class: none//

=**__Mathematical Reflections Inv. 4 Pg. 59__**= Graphs: 1.1/1.2 – The graph is linear because the line is straight. Y increases by a constant amount as x increases. It has a positive slope. 1.3 – The graph is linear. The slope isn’t as steep as the graph in 1.1/1.2. It has a positive slope. 3.1 – the graph is nonlinear. There is a y-intercept and the graph shows exponential growth as y increases while x increases.
 * 1. Look back at the graphs you have made in this unit. Find several graphs that show relationships in which y increases as x increases.**

1.4 – the graph is linear. It has a negative slope, and y decreases by a constant rate as x increases. 2.2 – the graph is nonlinear. It is curved and shows exponential decay as y decreases as x increases (not at a constant rate). 2.3 – the graph is nonlinear. It is curved and steeper at the beginning and less steep at the end. It shows exponential decay because y decreases as x increases, but not at a constant rate. 3.2 – the graph is nonlinear, curved, shows exponential decay. It’s steeper at the beginning. Y decreases as x increases.
 * 2. Look back at the graphs you have made in this unit. Find several graphs that show relationships in which y decreases as x increases.**

1.4 Follow-Up – the graph shows exponential growth in the beginning, and exponential decay later. The shape is an arc. The graph is nonlinear. 4.1 A2 – The graph has a strange shape. It is flat at the beginning and shows exponential growth, and then exponential decay as the graph’s line decreases, has a little bump, and continues decreasing in a curve. The graph is nonlinear. 4.1 B – the graph is nonlinear. It shows exponential growth as the line increases (not steeply) then gradually decreases. 4.1 D – the graph is nonlinear and increases gradually then stays somewhat flat and shows exponential decay.
 * 3. Look back at the graphs you have made in this unit. Find several relationships in which y both increases and decreases as x increases.**


 * Summary:** In this investigation I learned about exponential growth and decay. This investigation taught me how to make stories and situations to represent graphs (and vice versa).