The Natural Base, e Essential Questions

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Presentation transcript:

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

Examine the graph of f(n)= (1 + )n Examine the graph of f(n)= (1 + )n. The function has a horizontal asymptote. As n becomes infinitely large, the value of the function approaches approximately 2.7182818…. This number is called e. Like , the constant e is an irrational number. n 1

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}.

Simplify Using Properties of Exponents Simplify the expression.

Simplify Using Properties of Exponents Simplify the expression.

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

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

Lesson 9.3 Practice A