The Interactive Graph below needs the Java Plugin for your browser. Download it here. The plugin is perfectly safe. If you do NOT have the plugin you will not see the interactive graph within a large rectangle below the directions.

Please start with the video tutorial on the right to get some insight into the interactive Graph below.

-----------------------------------------
WHAT IS e?
-----------------------------------------

First, "e" is a number - an irrational number.As you may recall an irrational number cannot be expressed as a ratio, i.e. a fraction, of two integers. Another way of thinking about an irrational number is that it is a decimal number that does not terminate or repeat.

2.7182818284590452... is a representation of the number "e." But since the number "e" has an infinite number of digits and there is no pattern to these digits the best that we can do is use this estimate. But where does the number "e" come from. Well if you want to know watch this.

So where is the number "e" used? It is used in areas that need to "model" growth and decay. Business and science use this number. Populations seem to increase(growth) and decrease(decay) at certain rates. Radioactive materials like carbon 14 decrease in quantity(decay) over long periods of time. If you take out a loan from a bank, you pay back your loan at a certain rate that grows(growth) a banks profits over the period of your loan. If you make an investment with your money you can get a payback(growth) on your investment. All these various types of growth and decay can represented by formulas that use the number "e."

On your TI there is a button for "e." Push to get the "e" option. Then push the button to see the "estimation" of "e." Please remember that the number that you see is NOT "e" but an estimate of "e" since "e" is irrational.

-----------------------------------------
DIRECTIONS
-----------------------------------------

Below is the function f(x) = e^x .

- You will see a red point that you can manipulate with your mouse. You can drag the red point along the curve and see the points x value "projected" along the x-axis and the points y value "projected" along the y axis.

- Also, by right clicking your mouse on the graph you will bring up a menu system that allows you to adjust the Cartesian Coordinate System on which the interactive graph sits.

- Your goal is to be able to do the following:

a) Determine the domain by moving the red point and examining the projection of the x coordinate along the x axis.
b) Determine the range by moving the red point and examining the projection of the y coordinate along the y axis.
c) Determine on what intervals of x the function f(x) will be increasing or decreasing.

---------------------------------------------------------------------------------
INTERACTIVE TABLE AND GRAPH FOR y = e^x
---------------------------------------------------------------------------------

The INTERACTIVE TABLE AND GRAPH below needs the LIVE MATH PLUGIN for your browser. Download it here. The plugin is perfectly safe. If you do NOT have the plugin you will not see the interactive graph within a large rectangle below the directions.

I suggest that you use Firefox for the greatest flexibility in using Live Math.

-----------------------------------------
DIRECTIONS
-----------------------------------------

Below is the function f(x) = e^x , a table of ordered pairs for the function, a graph of points defined by the ordered pairs in the table and an "interpolated" curve going through the points. You have a number of ways to interact with the module below. Let me explain:

a) You can change the values of the "domain" in the table. There are two numbers initially in the domain below -4 and 4. Note that the first number in the domain, -4, MUST be less than the second number, in this case 4. Go ahead and see what happens if you change the domain - don't go crazy with super large numbers!

b) Due to what seems like a programming bug in Live Math you can change how many points you want but the number of points must be less than or equal to the original number of points which is 9. Go ahead and see what happens if you change the number of points- don't go crazy with a super large number!

c) You can determine how your x values will get incremented by changing the value of "inc".
Go ahead and see what happens if you change "inc"- don't go crazy with a super large number!

... Left click this icon. The go to the graph, left click, hold and then drag around a region that you want to zoom-in on, i.e. get closer to the graph.

...Left click on this icon and you will zoom out, i.e. move further away from the graph.