1. The Natural Base, e Essential Questions
How do we use the number e to write and graph exponential functions representing real-world situations?
Holt McDougal Algebra 2
Holt Algebra 2

2. Examine the graph of f(n)= (1 + )n
Examine the graph of f(n)= ( )n. The function has a horizontal asymptote. As n becomes infinitely large, the value of the function approaches approximately …. This number is called e. Like , the constant e is an irrational number. n 1

3. Exponential functions with e as a base have the same properties as the functions you have studied. The graph of f(x) = ex is like other graphs of exponential functions, such as f(x) = 3x.
The domain of f(x) = ex is all real numbers. The range is {y|y > 0}.

4. Simplify Using Properties of Exponents
Simplify the expression.

5. Simplify Using Properties of Exponents
Simplify the expression.

6. Evaluating Natural Base Expressions
Use a calculator to evaluate the expression. Round the result to three decimal places.

7. Recognizing Inverses
Simplify each expression.
12. lnex + 4y
13. e2ln(x+1)
11. lne0.15x
logee0.15x
logeex + 4y
eloge(x + 1)2
0.15x
x + 4y
(x + 1)2
14. lne2x + lnex
15. e2ln (8x)
logee2x
+ logeex
eloge(8x)2
2x + x
64x 2

8. Lesson 9.3 Practice A