Decay in Math

Decay in math refers to the process of decreasing or diminishing over time. It is commonly used in the context of exponential functions and decay models. Understanding decay is important in various real-life applications such as population growth, radioactive decay, and depreciation of assets.

Exponential Decay

Exponential decay occurs when a quantity decreases at a constant percentage rate over a period of time. The general formula for exponential decay is given by:

A = A₀ * e^-rt

Where:

• A = the final amount after time t
• A₀ = the initial amount at time t = 0
• r = the decay rate (as a decimal)
• t = time
• e = Euler's number (approximately 2.71828)

Study Guide

To understand and solve problems related to decay, here are the key concepts to focus on:

1. Understanding the concept of exponential decay and its application in real-life situations.
2. Recognizing the decay rate (r) and how it affects the rate of decrease over time.
3. Using the exponential decay formula to solve problems involving decay, such as finding the amount of a substance remaining after a certain time period.
4. Practicing with word problems and scenarios involving decay, such as radioactive decay or the depreciation of assets.

By mastering these concepts, you'll be well-prepared to tackle problems related to decay and exponential functions in your math studies.