4.2 Exponential Growth and Decay

In this lesson, you will learn about Exponential Growth and Decay.

Lesson Objectives

• Verify that exponential functions of the form f(t)=Cekt are solutions to the differential equation  f'(t)=kf(t).
• Solve differential equations of the form f'(t)=kf(t).
• Calculate doubling time and half-life.
• Model and solve applications involving exponential growth and decay.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

1. YouTube video: Exponential Growth Calculus Version
3. YouTube video: Exponential Decay Formula Proof
4. YouTube video: Introduction to Exponential Decay
5. YouTube video: More Exponential Decay Examples
6. YouTube video: Word Problem Solving – Exponential Growth and Decay

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

1. 8.7 Exponential Growth and Decay  – exponential growth models, applications of exponential growth, exponential decay models, and applications of exponential decay
2. Section 9.4: Exponential Growth and Decay  – the definition of an exponential function, population modeling, radioactive decay, Newstons law of cooling, compounding of interest
3. Exponential Growth and Decay  – examples of exponential growth or decay, a useful differential equation, a problem, half-life

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

1. Applications of Exponential Functions
2. 3.2 Exponential Growth and Decay: Quiz  (5 problems with answers)
3. 7.4 Exponential Growth and Decay  (with answers and solutions)
4. Practice with Applied Exponential Growth and Decay  (with answers)
5. Investigate these equations for exponential growth and decay