Lesson 1: Understanding Exponential Functions

• What is an exponential function?
• How do exponential functions grow?
• What's the difference between linear and exponential?
• What does the base mean in an exponential function?

Exponential function, base, exponent, growth, decay, constant ratio

CCSS.MATH.9.F.LE.A.1

Description: Exponential functions are introduced as functions where the variable is in the exponent (f(x) = a × b^x). Students compare exponential growth (like doubling) to linear growth (adding the same amount). Using real-world examples (bacteria doubling, population growth, radioactive decay), they see why exponential functions are important. Purpose: To establish foundational understanding of exponential functions and their real-world relevance. DOK Level: 1-2 (Recall and Understanding)

• Real-world contexts: Use relatable scenarios (doubling, halving)
• For struggling learners: Focus on simple bases (2, 3) and positive exponents
• For advanced learners: Include fractional bases and negative exponents
• Comparison tables: Show linear vs. exponential side-by-side

• Observation: Can students identify exponential functions?

• Sorting activity: Classify functions as linear or exponential

• Comparison task: Create tables showing linear vs. exponential growth

• Exit ticket: Explain what makes a function exponential

• Exponential function examples (written and on cards)

• Linear vs. exponential comparison tables

• Real-world context cards

• Anchor chart for exponential functions

• Resource: Khan Academy "Exponential Functions" (adapted)