Writing Exponential Functions from Data Tables

Miacademy & MiaPrep Learning Channel

This instructional video guides students through the process of writing exponential functions from data tables, building upon previous knowledge of reverse-engineering functions from graphs. The narrator, Justin, systematically demonstrates how to identify the initial value (a) and the growth or decay factor (b) to construct equations in the form f(x) = a tb^x. The video contrasts tables with graphs, highlighting that tables offer precise numerical values which can make function writing more accurate. The content progresses through three distinct examples of increasing complexity: (1) a basic table with consecutive integer inputs starting at zero; (2) a table with inputs increasing by intervals of three, introducing fractional exponents; and (3) a table where the initial value (x=0) is missing, requiring students to work backward. Key mathematical themes include calculating growth factors by dividing consecutive outputs, handling non-unit intervals using roots or fractional exponents, and extrapolating data to find unknown initial values. This resource is highly valuable for Algebra 1 and Algebra 2 classrooms as it directly addresses common student stumbling blocks, such as what to do when the y-intercept isn't explicitly given or when data points aren't consecutive. It provides clear, step-by-step procedural knowledge that allows teachers to scaffold learning from simple pattern recognition to more complex algebraic manipulation involving roots and exponents.