2.4

Topic

Exponential Function Manipulation Exponential functions model growth patterns where successive output values over equal length input-value intervals are proportional. When the input values are whole numbers, exponential functions model situations of repeated multiplication of a constant to an initial value. 2.5.A.2 A constant may need to be added to the dependent variable values of a data set to reveal a proportional growth pattern. 2.5.A.3 An exponential function model can be constructed from an appropriate ratio and initial value or from two input-output pairs. The initial value and the base can be found by solving a system of equations resulting from the two input-output pairs. 2.5.A.4 Exponential function models can be constructed by applying tr o ansformations t f x( ) = ab x based on characteristics of a contextual scenario or data set. 2.5.A.5 Exponential function models can be constructed for a data set with technology using exponential regressions. 2.5.A.6 The natural base e, which is approximately 2.718, is often used as the base in exponential functions that model contextual scenarios.