PPT-Exponential and Logarithmic Functions

Exponential Functions amp Their Graphs Logarithmic Functions amp Their Graphs Properties of Logarithms Exponential and Logarithmic Equations Exponential and Logarithmic Models a b. Exponential Growth Functions. If a quantity increases by the same proportion . r. in each unit of time, then the quantity displays exponential growth and can be modeled by the . equation. Where. C = initial amount. Exponential Function. f(x) = a. x. . for any positive number . a. other than one.. Examples. What are the domain and range of. . y = 2(3. x. ) – 4?. What are the. roots of . 0 =5 – 2.5. x. ?. Reva . Narasimhan. Associate Professor of Mathematics . Kean University, . NJ. www.mymathspace.net/presentations. Overview. Introduction . Why functions?. Challenges in teaching . the function concept. T. rigsted - Pilot Test. Dr. Claude Moore - Cape Fear Community College. CHAPTER 5: . Exponential and Logarithmic Functions and Equations. 5.1 Exponential Functions. 5.2 The Natural Exponential Function. Differentiation. Integration. Properties of the Natural Log Function. If a and b are positive numbers and n is rational, then the following properties are true:. The Algebra of Logarithmic Expressions. A Global View. Gretchen A. Koch. Goucher College. PEER UTK 2011. Special Thanks To:. Dr. Claudia . Neuhauser. University of Minnesota – Rochester. Author and creator of modules. Learning Objectives. Chapter 1.3. The Exponential Function. DEFINITION:. Let a be a positive real number other than 1. The function. is the . exponential function with base a. ..  . 2. The Exponential Function. The domain of an exponential function is . Chapter 3 Section 5. Quick Review. . Quick Review Solutions. . What you’ll learn about. Solving Exponential Equations. Solving Logarithmic Equations. Orders of Magnitude and Logarithmic Models. Newton’s Law of . Date: ______________. Warm-Up. Rewrite each percent as a decimal.. 1.) 8% 2.) 2.4% 3.) 0.01%. 0.08 0.024 0.0001. Evaluate each expression for x = 3.. 4.) 2. x. 5.) 50(3). x. 6.) 2. Differentiate between linear and exponential functions.. 4. 3. 2. 1. 0. In addition to level 3, students make connections to other content areas and/or contextual situations outside of math..  . Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model.. 3.2 Exponential growth and decay: Constant percentage rates. 1. Learning Objectives:. Understand exponential functions and consequences of constant percentage change.. Calculate exponential growth, exponential decay, and the half-life.. molecular dynamics systems of coupled harmonic oscillators n = 2 or 3 n �� 1 continuum exponential growth and decay molecular dynamics systems of coupled harmonic oscillators Power . Exponential Notation. A short hand of writing a number with out changing its Value. It only changes the way it looks.. * . . . . .  . X10. #. x10. - #. Number gets larger . All slides in this presentations are based on the book Functions, Data and Models, S.P. Gordon and F. S Gordon. ISBN 978-0-88385-767-0. Fitting Data to An Exponential Function. Although Linear Regression is a powerful tool, not all relationships between two quantities are linear. (See scatterplots in figure 5.28).