Mathematical+Reflections,+p.60

Tuesday, January 14th, 2008 Z.K. ==== **Big Idea:**    The rate at which many things grow or decay can often be described mathematically. ====

** Essential Question: **
How can I model a pattern of repeated division?

**Notes from Class:**

**Mathematical Reflection** //Investigation Four//


 * 1. How can you recognize an exponential decay pattern from a table of data? From a graph? From an equation?**

You can recognize exponential decay patterns in…

From a table if the numbers are decreasing, then take a ratio of two y-values at a time. If you do this a few times and the ratio is the same, than you know the graph is exponential decay. Make sure the y-values you pick are next to each other. Don’t skip a few numbers and pick the first and last numbers or something.

From a graph, if the line goes from left to right in a downwards curve shape then it is an exponential decay pattern.

From an equation the variable has to be greater than zero and the base should be between zero and one.

y = a(b^x)

a is the variable

b is the base


 * 2. How is the table of an exponential decay situation different from a table of an exponential growth situation? How is the graph different? How is the equation different?**

For an exponential decay pattern, the ratio of the two numbers has to be a positive number but the value must be less than one.

For an exponential growth pattern the ratio of the two numbers has to be greater than one.


 * 3. How are patterns in tables, graphs, and equations for decay situations similar to and different from tables, graphs, and equations for decreasing linear relationships?**

The similarities include:

The graphs both go downwards from a left to right pattern.

The numbers in the y-value of tables decrease.

There is a constant ratio if two values are measured in the tables, and the ratio is always a number bellow one.

The differences include:

Though both types of graphs go downwards, in a linear relationship the line is straight and in exponential decay the line is a curve shape.

Linear equations don’t have exponents, exponential decay equations do.

**Summary:**

In this investigation I learned what exponential decay is and how to graph the data for decay. I also learned how to take a decay graph or table and how to turn that data into an equation.