PPT-FBI Challenge: Exponential

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. 118 brPage 2br Exponential Stability The origin of is exponentially stable if and only if the linearization of at the origin is Hurwitz Theorem Let be a locally Lipschitz function de64257ned over a domain Let be a continuously differentiable functi Exponential . 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. 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. ?. 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 . 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. 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.. 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.. Paired with name. Exponential Entrepreneur. Exponential entrepreneur is a yearlong course, which is part of a three year long program designed to introduce students to current technologies that are growing at exponential rates. . 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).