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Unit 6 — Exponents and Exponential Functions

Unit 6 · Exponents & Exponential Functions

Exponents & Exponential Functions

Master exponent rules, scientific notation, rational exponents, and radicals — then use exponential functions to model real-world growth and decay.

Estimated Time

30–40 minutes

Difficulty

Intermediate

7 Lessons
7 Learning Goals
10 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 6 — Exponents & Exponential Functions gives you the tools to work with powers. You will master all exponent rules, convert between scientific notation and standard form, simplify radical expressions, and model real-world growth and decay with exponential functions.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Apply the product, quotient, power, zero, and negative exponent rules to simplify expressions.
Goal 2Write numbers in scientific notation and perform operations with them.
Goal 3Convert between radical form and rational exponent form and simplify radical expressions.
Goal 4Identify, evaluate, and graph exponential functions of the form f(x) = ab^x.
Goal 5Model real-world growth and decay situations with exponential functions.
Goal 6Apply percent change and compound interest formulas to solve problems.
Goal 7Compare linear and exponential functions using tables, graphs, equations, and real-world contexts.

Skills You Will Master

Exponent rules
Scientific notation
Radicals & rational exponents
Graphing exponential functions
Growth & decay models
Compound interest

Real-World Connection

Exponential functions are one of the most powerful models in all of science and finance. Bacteria populations double at a constant rate — exponential growth. Radioactive materials decay at a constant rate — exponential decay. Money in a savings account grows with compound interest — an exponential function. Social media posts go viral exponentially. Understanding exponents and exponential functions gives you the mathematical tools to describe any process that grows or shrinks by a constant percentage over time.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter
Unit 6Unit Overview6.1 · Exponent Rules