Introduction
If you are a budding environmental scientist, archaeologist, physical scientist, or bacteriologist then this is the section for you. This is where we will be looking at the differential equation of proportional change and how it is related to the laws of decay and growth. This one equation is incredibly important in the sciences.
Objective: We address topic 3 (pdf) in the AP course outline. By the end of this section you will be able to solve equations describing exponential growth and decay. You will also be able to use other differential equations such as Newton’s Law of Cooling and Compound interest formulas.
Topics in this section include:
- 6-4.1 The Law of Exponential Change
- 6-4.2 Growth and Decay - Examples
- Video: Differential Equation Model
- 6-4.2.1: Differential Equations - Separation of Variables
- Check for Understanding
- 6-4.3 Radioactivity and Half-life
- Practice Online: Exponential Growth and Decay
- Racetrack Activity: A Day at the Races
- 6-4.4 Compound Interest
- 6-4.5 Newton’s Law of Cooling
- 6-4.6 Resistance Proportional to Velocity
Guiding Questions
As you navigate through this section, ask yourself the following questions:
- What are some real-life examples of growth or decay that you have seen reference to in the news this year?
- Which grows faster, a population whose growth follows the equation y = kx or the one that follows the equation y = kex? Why?
Now that you are familiar with the topics we will cover in this section of Module 6, you are ready to begin. Please click the menu item under Section called The Law of Exponential Change to begin 6-4.1 The Law of Exponential Change.
Photo Attribution
Description: A female student examining liquid in a beaker as she conducts a science experiment
Source: iStock.com