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. 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 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. ?. 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. . 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. 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. 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 . A. Vocabulary:. Power . – product in which the factors are the same. Exponent . – tells how many times the . base . is multiplied. Base . – the number that is multiplied. Exponential notation . 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).