1. What is Exponential Decay?

Exponential decay describes the process of reducing an amount by a consistent percentage rate over time. It's commonly used in physics, chemistry, finance, and many other fields to model processes like radioactive decay, depreciation, and population decline.

2. How Does the Calculator Work?

The calculator uses the exponential decay formula:

Where:

• \( initial \) — Starting value or quantity
• \( decay\_rate \) — The rate of decay per time period (as a decimal between 0 and 1)
• \( time \) — Number of time periods elapsed
• \( value \) — Remaining value after decay

Explanation: The formula calculates how much of the original quantity remains after undergoing constant percentage decay over a given time period.

3. Applications of Exponential Decay

Details: Exponential decay models are used in radioactive decay calculations, drug metabolism in pharmacology, depreciation of assets in finance, cooling/heating processes in thermodynamics, and population decline in biology.

4. Using the Calculator

Tips: Enter the initial value, decay rate (as a decimal between 0 and 1), and time period. All values must be positive numbers (decay rate must be ≤1).

5. Frequently Asked Questions (FAQ)

Q1: How is decay rate different from half-life?
A: Decay rate is the percentage lost per time period, while half-life is the time for half the quantity to decay. They're related but different concepts.

Q2: Can decay rate be greater than 1?
A: No, a decay rate greater than 1 would imply more than 100% loss per period, which isn't meaningful in decay contexts.

Q3: What if I know the half-life instead of decay rate?
A: You can convert half-life to decay rate using: decay_rate = 1 - 0.5^(1/half_life).

Q4: Does this work for continuous decay?
A: This formula models discrete decay. For continuous decay, use the natural exponential form: value = initial × e^(-λt).

Q5: How accurate is this model for real-world applications?
A: It's accurate for processes with constant percentage decay. Some real-world processes may require more complex models.