Comparing Linear and Exponential Growth Models

Miacademy & MiaPrep Learning Channel

This educational video clarifies the fundamental differences between linear and exponential growth models through visual representation. Building on previous concepts of slope, the narrator, Justin, transitions from analyzing numerical data tables to interpreting graphical models. The video explicitly demonstrates how linear data produces a straight line with a constant slope, while exponential data creates a curve that becomes progressively steeper, illustrating why a single slope value is insufficient for modeling exponential growth. Key themes include data analysis, graphical modeling, and pattern recognition. The video contrasts the additive nature of linear growth (constant rate of change) with the multiplicative nature of exponential growth (changing rate of change). It introduces the concept of a mathematical "model" as a visual line or curve that represents a set of data points, emphasizing how to match specific data behaviors—like adding a constant versus multiplying by a factor—to their corresponding visual shapes. Ideally suited for Algebra I classrooms, this resource helps students bridge the gap between abstract numerical tables and visual graphs. It addresses the common student struggle of distinguishing functions based on data behavior alone. Teachers can use this video to introduce graphing exponential functions or as a review tool to reinforce the visual distinctions between linear and exponential relationships before moving on to complex real-world applications.