SAT Math: Choosing Between Linear and Exponential Models
30+ practice questions in Praczo
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.
- ✗ 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.
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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