LAC 28:CXLII.2117. Linear, Quadratic, and Exponential Models

A. Construct and compare linear, quadratic, and exponential models and solve problems. 1. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals. b. Prove that exponential functions grow by equal factors over equal intervals. c. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. d. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs. 3. Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically, with and without technology. B. Interpret expressions for functions in terms of the situation they model. 1. Interpret the parameters in a linear, quadratic, or exponential function in terms of a context.