1. Objectives: 1. Be able to find the Euler Number. 2.Be simplify expressions using the Natural base (with a calculator also) 3.Be able to graph a Natural Base Exponential. Objectives: Euler Number, Natural base

2. Value of “n”FormulaValueSignificance Annually Semi-Annually Quarterly Monthly Daily Hourly Minutely 31,536,000 1 2 4 12 365 8,760 525,600 2 2.25 2.44140625 2.61303529 2.714567482 2.718126691 2.718279215 2.718282473 Secondly Use the expression to fill in the table: I. The Euler Number

3. II. The Natural Base The Natural Base e: The natural base e is irrational. It is defined as follows: As n approaches ∞ approaches e ≈ 2.718281828 Directions: Simplify the natural base expressions 1. e 2 e 5 e 2+5 e7e7 2. 4e 4-3 4e 3. (5e -3x ) 2 5 2 e -6x Directions: Evaluate each expression with a calculator 1. e 7 1096.633158 2. e 3/4 2.117000017

4. III. Graphing a Natural Base Exponential Function Form: f(x) = ae rx If a > 0 and r > 0, then the function is an exponential growth If a > 0 and r < 0, then the function is an exponential decay

5. Graph: f(x) = 3e.25x Exponential Growth x f(x) 0 3 1 3.85 2 4.95 2.34 -2 1.82 Domain: All Real Numbers Range: y > 0 III. Graphing a Natural Base Exponential Function

6. Graph: f(x) = e.-0.75(x - 2) + 1 Exponential Decay x f(x) 2 2 3 1.47 4 1.22 1 3.12 0 5.48 Domain: All Real Numbers Range: y > 1 III. Graphing a Natural Base Exponential Function

7. Page 495-496 #3-49 odd (24 problems) DOMAIN AND RANGE ON ALL GRAPHS!!!!!

8. Use the expression to fill in the table: I. The Euler Number Value of “n”FormulaValueSignificance 31,536,000 1 2 4 12 365 8,760 525,600