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Linear Growth and Decay (SAT)

Mathematics SAT Reasoning Test Math section Difficulty 2/5

Beginning of the lesson

Linear Growth and Decay

SAT Math — Algebra & Problem Solving | Master the most frequently tested linear model concepts

1. Linear vs. Exponential — Know the Difference

📈 Linear
  • Constant AMOUNT added or subtracted each period
  • "Increases by 50 each year"
  • "Decreases by 3 per hour"
  • Formula: y = mx + b
  • Graph: Straight line
📈 Exponential
  • Constant PERCENT multiplied each period
  • "Increases by 5% each year"
  • "Doubles every 3 hours"
  • Formula: y = a · bt
  • Graph: Curved line
🚨 SAT TRAP: "Increases by 10" → LINEAR (adds 10). "Increases by 10%" → EXPONENTIAL (multiplies by 1.10). Read carefully — one word changes everything!
Visual Comparison: Linear vs. Exponential Growth
Interactive visualization — available in the full lesson

Notice: The linear function is a straight line. The exponential function curves upward, eventually growing much faster.

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  • Worked examples
  • Common mistakes and how to avoid them
  • Test questions: 187
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