CurriculumGrade 9Mathematics

Linear and Exponential Models

Aligned to F-LE.A.1 — Common Core State Standards for Mathematics.

What this lesson teaches

Linear growth adds the same amount each step, while exponential growth multiplies by the same factor each step. That is why exponential growth starts slow but eventually shoots far past linear growth. You choose the model that matches how a quantity changes.

Worked example

Adding $10 each week is linear: $10, $20, $30. Growing 10% each week is exponential: $100, $110, $121, with each step multiplied by 1.1.

Practice questions

  1. Is doubling every day linear or exponential?
  2. Write a linear rule for starting at 5 and adding 3 each step.
  3. Why does exponential growth eventually pass linear growth?

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

▶ Watch this lesson

En español

Modelos Lineales y Exponenciales

El crecimiento lineal suma la misma cantidad en cada paso, mientras que el crecimiento exponencial multiplica por el mismo factor en cada paso. Por eso el crecimiento exponencial empieza despacio pero con el tiempo supera con creces al crecimiento lineal. Eliges el modelo que mejor describe cómo cambia una cantidad.

Ejemplo: Agregar $10 cada semana es lineal: $10, $20, $30. Crecer un 10% cada semana es exponencial: $100, $110, $121, donde cada paso se multiplica por 1.1.

Teach this lesson today

An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.

Start free — no card required