PPT-Section 9.2 Exponential Functions

Evaluating Rational amp Irrational Exponents Graphing Exponential Functions fx a x Equations with x and y Interchanged Applications of Exponential Functions Use calculators to calculate graphing points. 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. Exponential Functions & Their Graphs. Logarithmic Functions & Their Graphs. Properties of Logarithms . Exponential and Logarithmic Equations. Exponential and Logarithmic Models. a. b.. 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 . (4.1) Exponential & Logarithmic Functions in Biology. (4.2) Exponential & Logarithmic Functions: Review. (4.3) . Allometry. (4.4) Rescaling data: Log-Log & Semi-Log Graphs. Recall from last time that we were able to come up with a “best” linear fit for . Exponential and Logarithmic Functions and Equations. 5.1 Exponential Functions. 5. .2 The Natural Exponential Function. 5.3 Logarithmic Functions. 5.4 Properties of Logarithms. 5.5 Exponential and Logarithmic Equations . We know:. 2. 3. =. 8. and. 2. 4. =. 16. But, for what value of . x. does. 2. x. = 10?. To solve for an exponent, mathematicians defined . logarithms. .. Since 10 is between 8 and 16, . x. must be between 3 and 4.. Section 3-1. The . exponential function f. with base . a. is defined by. . f. (. x. ) = . a. x. where . a. > 0, . a. .  1, and . x. is any real number.. For instance, . . f. (. x. ) = 3. Graphs of Logarithmic Functions . Log. 2. x. Equivalent Equations. Solving Certain Logarithmic Equations. 9.3. 1. Inverses of Exponential Functions. f(x) = 2. x. f. -1. (x) = ? x = 2. y. 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.. 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.. Growth of Product . U. sing Polymerase Chain Reaction (PCR). Intro. Using math to solve a biological science problem. Students will use their knowledge of:. Exponential equations. Molecular biology. HS Biology Standards. 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).