Up to this point you have worked with rational bases. However, exponential functions can have irrational bases as well. One important irrational base is the number e. The graph of y = ( 1 + 1 x ) x y equals . open . 1 plus , 1 over x . close to the x  has an asymptote at y = e y equals e  or y ≈ 2.71828.

Natural base exponential functions are exponential functions with base e. These functions are useful for describing continuous growth or decay. Exponential functions with base e have the same properties as other exponential functions.

Problem 4 Evaluating e x e to the x

How can you use a graphing calculator to evaluate e 3 ? e cubed , question mark

Think

After you press the e x e to the x  key, what keys should you press?

Press 3 , begin box , 3 , end box comma   ) , begin box , close , end box comma  and enter . begin box , enter , end box , .

Method 1	Method 2	Method 3
Use the e x e to the x  key.	Use the graph of y = e x . y equals , e to the x , .	Use a table of values for y = e x . y equals , e to the x , .
		Image Long Description

e 3 ≈ 20.086 e cubed , almost equal to , 20.086

✓ Got It?

4. How can you use a graphing calculator to calculate e 8 ? e to the eighth , question mark

In Lesson 7-1 you studied interest that was compounded annually. The formula for continuously compounded interest uses the number e.

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