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### Linear, Quadratic, and Exponential Models

 Standard Essential Question Bloom’s Taxonomy Activities Vocabulary Pacing F.LE.1 Distinguish between situations that can be modeled    with linear functions and with exponential functions. What is the difference between the progression of points on a linear graph and the progression of points on an exponential graph? -Given a situation, determine if the model created is linear or exponential based on the context clues in the equation. -Linear graph -Exponential graph 3 days F.LE.1a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. How many points are needed to create an accurate equation for a linear function and an accurate equation for an exponential function? Are there exceptions? -Given the graph of a linear function, defend algebraically or graphically that the function increases or decreases over equal intervals by equal quantities. -Given the graph of an exponential function, prove growth occurs over equal intervals. -Interval -Equal factor -Equal difference 3 days F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. What context clues suggest that a quantity changes at a constant rate per interval? -Analyze several word problems relating to constant rate of change to determine which qualities or context clues are consistent across the problems. -Constant rate 3 days F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. What context clues suggest that a quantity changes at a constant factor per interval? -Analyze several word problems relating to constant factors of change to determine which qualities or context clues are consistent across the problems. -Constant factor 3 days F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table). What information is necessary to create a graphical or algebraic representation of a described function? -Given various expressions of information pertaining to a linear or an exponential function, create a graphical or algebraic representation of the function. -Input-output pairs 3 days F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. What is unique about an exponential function as compared to a linear or quadratic function? -Analyze linear, quadratic, and exponential functions to determine unique qualities between the three types of functions. -Exponential function -Linear function -Quadratic function 3 days F.LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. In what instances is 2+2 not equal to 4? -Self-guide your understanding of logs using the graphing calculator; create your own problems and share with the class http://mathbits.com/mathbits/tisection/Algebra2/logarithms.htm -Logarithm -Base -Exponent -Natural log 3 days F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. How does the manipulation of the components of a function relate to its corresponding graph? -Given a function, manipulate various components such as slope or intercept to determine how the function changes under the new conditions. -Parameters 1 day