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Exponential and Comparing Functions

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you compare linear, quadratic, and exponential functions across tables, graphs, and contexts to decide which model fits?

Compare and contrast linear, quadratic, and exponential functions using tables, graphs, and equations, and determine which family best models a situation (A.F.2).
A Virginia SOL Algebra I answer on comparing function families: constant differences (linear), constant second differences (quadratic), and constant ratios (exponential), the shapes of their graphs, and choosing a model.
9 min answer →

What is an exponential function, how do you recognize it from a table or graph, and how do you interpret its initial value and growth factor?

Identify and interpret exponential functions of the form f(x) = ab^x from tables, graphs, equations, and contexts, including the initial value and the constant growth or decay factor (A.F.2).
A Virginia SOL Algebra I answer on exponential functions: the form f(x) = ab^x, recognizing a constant multiplier in a table, the initial value a and base b, and the shape of an exponential graph.
9 min answer →

How do you model and solve exponential growth and decay problems using the percent-change form?

Model and interpret exponential growth and decay using the form y = a(1 + r)^t for growth and y = a(1 - r)^t for decay, and evaluate to solve real-world problems (A.F.2).
A Virginia SOL Algebra I answer on exponential growth and decay: the percent-change models y = a(1 + r)^t and y = a(1 - r)^t, converting a percent rate to a multiplier, and solving applied problems.
9 min answer →

How do you identify and find terms of arithmetic and geometric sequences using the explicit formulas?

Distinguish arithmetic from geometric sequences and use the explicit nth-term formulas to find terms and relate sequences to linear and exponential functions (A.F.2).
A Virginia SOL Algebra I answer on arithmetic and geometric sequences: the common difference and common ratio, the explicit nth-term formulas on the formula sheet, and the link to linear and exponential functions.
9 min answer →