Key Components of Exponential Decay

1. Initial Quantity (P): The initial amount of the quantity at time t=0.
2. Decay Factor (r): The rate at which the quantity decreases per unit time. It is a fraction between 0 and 1, where 0 < r < 1.
3. Time (t): The duration over which the quantity is decaying.
4. Final Quantity (A): The amount of the quantity remaining at time t.

Exponential Decay Formula

The exponential decay formula is given by:

A = P * (1 - r)^t

Where:

• A = Final quantity
• P = Initial quantity
• r = Decay factor
• t = Time

Example Problem

Suppose a radioactive substance decays at a rate of 20% per hour. If the initial quantity of the substance is 100 grams, how much will remain after 5 hours?

Using the exponential decay formula:

A = 100 * (1 - 0.20)^5

A ≈ 100 * (0.8)^5

A ≈ 100 * 0.32768

A ≈ 32.768 grams

Study Tips for Exponential Decay

• Understand the concept of decay factor and its relationship to the rate of decay.
• Practice using the exponential decay formula with different values of P, r, and t.
• Use graphing calculators or software to visualize exponential decay curves.
• Explore real-world applications of exponential decay in fields such as population growth, radioactive decay, and investment depreciation.