PPT-8-8 Exponential Growth and Decay

RULE Exponential Growth Modeling Exponential Growth In 1998 a certain town had a population of about 13000 people Since 1998 the population has increased about 14 a year Write an equation to model the population increase. Understanding the difference. Linear equations. These equations take the form:. . y. = . mx. + . b. . . m. is the slope of the line. . b. is the value of . y. when . x. = 0 . (the . y. - . Fernando . G.S.L. . Brand. ão. ETH Zürich. Based on joint work with . Michał. . Horodecki. Arxiv:1206.2947. COOGEE. 2013. Condensed (matter) version of the talk. Finite correlation length implies correlations are short ranged. Exponential Functions & Their Graphs. Logarithmic Functions & Their Graphs. Properties of Logarithms . Exponential and Logarithmic Equations. Exponential and Logarithmic Models. a. b.. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License. . Skills. : none. C. oncepts. : linear growth, exponential growth, linear scale plot, logarithmic scale plot, “hockey . State that radioactive decay is a random and spontaneous process and that the rate of decay decreases exponentially with time.. Define the term radioactive half-life. . Determine the half-life of a nuclide from a decay curve. . Section 6.4a. Law of Exponential Change. Suppose we are interested in a quantity . . . that . increases or. decreases at a rate proportional to the amount present…. Can you think of any examples???. 8. What you Should Learn. I can interpret coefficients and exponents in the context of the problem.. I can model and solve growth (appreciation) and decay (depreciation) problems.. Exponential Growth. 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..  . The decay rate.  . Lorentz Invariant Phase Space. The decay rate.  . The decay rate.  . Decay amplitude. Describes the interactions during the decay.. The Feynman diagrams. The Feynman diagrams. Exponential Growth. (J-shaped curve). Logistic Growth. (S-shaped curve). Population ecology. Population ecology is the study of populations.. Population . = group of individuals of the same species occupying a common geographical area. 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 . GROWTH. Growth. defined as the increase in size of an organism or of its parts due to the synthesis of . Protoplasm. (includes both cytoplasm and nucleus) or . Apoplasmatic. substances . (substance produced by cells and forms a part of the tissues . 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).