MathAdvanced MathHigh frequency

SAT Math: Choosing Between Linear and Exponential Models

30+ practice questions in Praczo

What you need to know

The concept, explained

  • 1

    Linear model: changes by the same fixed amount each period (constant rate of change). Graph is a straight line.

  • 2

    Exponential model: changes by the same percentage each period (constant growth/decay factor). Graph curves.

  • 3

    To identify from a table: calculate successive differences (linear) or successive ratios (exponential).

  • 4

    Real-world cues: "grows by $50/year" → linear. "grows by 5%/year" → exponential.

  • 5

    Exponential growth eventually dominates linear growth, no matter how large the linear rate.

Common mistakes
  • Seeing a percentage and assuming exponential when the context means a fixed dollar amount representing a percent of a fixed base.
  • Using a linear model for a scenario that compounds — like interest that builds on accumulated interest.
Try a sample question

SAT-style practice

A town grows by 200 people per year. A second town grows by 4% per year. Both start at 5,000. Which model describes the second town?

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