PPT-P, NP, and Exponential Problems

Should have had all this in CS 252 Quick review Many problems have an exponential number of possibilities and we can try each option against some objective to get an answer Note that this testing is fast always polynomial. Sebastián Jordán, Valentina Carvajal, Rebeca Pérez-Anda, Juan Ignacio . Lalama. 04/15. Introduction. The Condor, is an important animal, . People have damaged most of the condor population.. T. h. 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. - . 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. By: . Enriqueta Ramirez and . Johnny Reyes. Acknowledgments. Susan B. Taber. . Using Alice in Wonderland to Teach Multiplication of Fractions. Kat Cain. . Lesson Template. Exponents in Wonderland. 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 . The inverse of an exponential function is a . logarithmic function. .. y = log . b . a. Read. :. . y = “log . base . b. . of . a”. Definition. log. b. . A = x is read as “log base b of a equals X.. Evaluating Rational & Irrational Exponents. Graphing Exponential Functions . f(x) = a. x. Equations with . x. and . y. Interchanged. Applications of Exponential Functions. Use calculators to calculate graphing points. 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. Exponential Growth. Exponential growth. occurs when an quantity increases by the same rate . r. in each period . t. . When this happens, the value of the quantity at any given time can be calculated as a function of the rate and the original amount. . 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.. 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. . 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.. 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).