Unit 4 · Exponential & Logarithmic Functions

Exponential & Logarithmic Functions

Master exponential growth and decay, logarithmic properties, natural log, and solving exponential and logarithmic equations — the mathematics behind finance, biology, and information theory.

Estimated Time

4–5 weeks

Difficulty

Intermediate

8 Lessons

8 Learning Goals

14 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 4 — Exponential & Logarithmic Functions is the mathematics of change at scale. You will explore exponential growth and decay, compound interest, and the natural base e, then study logarithms as the inverse of exponential functions. The unit closes with solving exponential and logarithmic equations and fitting exponential models to real data.

Learning Objectives

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

Goal 1Evaluate and graph exponential functions, identifying key features including asymptotes and intercepts.

Goal 2Apply exponential models to growth, decay, and compound interest problems.

Goal 3Define logarithms as inverses of exponential functions and convert between exponential and logarithmic form.

Goal 4Graph logarithmic functions and describe their transformations and asymptotes.

Goal 5Apply the product, quotient, and power rules to expand and condense logarithmic expressions.

Goal 6Solve exponential and logarithmic equations using properties of logarithms and the change-of-base formula.

Goal 7Build and interpret exponential models for real-world data including population, radioactive decay, and finance.

Goal 8Fit exponential models to data using regression and evaluate the quality of fit.

Skills You Will Master

Exponential growth & decay

Logarithmic functions & graphs

Logarithm properties

Solving exp & log equations

Real-world modeling

Fitting exponential models to data

Real-World Connection

Exponential and logarithmic functions are the mathematics of change at scale. Compound interest uses exponential growth to calculate savings and loan balances. Radioactive dating uses exponential decay to determine the age of fossils and artifacts. The Richter scale and decibel scale are logarithmic — each step represents a tenfold increase in intensity. Information theory, which underlies every digital device, is built on logarithms. Mastering Unit 4 gives you the tools to model any process that grows or shrinks by a constant percentage.

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

3.10 · Unit 3 ReviewUnit Overview4.1 · Exponential Functions