PPT-Linear vs. Exponential Graphing

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 . N is the process noise or disturbance at time are IID with 0 is independent of with 0 Linear Quadratic Stochastic Control 52 brPage 3br Control policies statefeedback control 0 N called the control policy at time roughly speaking we choo e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations 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: Christine Berg. Edited By: VTHamilton. Linear Equation. An equation for which the graph is a line. Solution. Any ordered pair of numbers that makes a linear equation true.. (9,0) IS ONE SOLUTION. Exponential Functions & Their Graphs. Logarithmic Functions & Their Graphs. Properties of Logarithms . Exponential and Logarithmic Equations. Exponential and Logarithmic Models. a. b.. 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 . 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. . Objectives:. To solve a system of linear equations by graphing. To classify a system of linear equations as consistent (independent and dependent) or inconsistent. To graph a system of linear inequalities. 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.. 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 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. Scientist interpret tables, graphs, and diagrams to locate data, examine relationships in the data, and extend those relationships beyond the data.. Reading graphs can be like reading a foreign language though. It come easy to some and very difficult to others..