1. What is Exponential Decay?

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value. It's commonly used to model radioactive decay, population decline, and depreciation of assets.

2. How Does the Calculator Work?

The calculator uses the exponential decay formula:

Where:

• \( y \) — Remaining amount (same units as initial amount)
• \( a \) — Initial amount
• \( r \) — Decay rate (between 0 and 1)
• \( t \) — Time elapsed

Explanation: The formula calculates the remaining quantity after time t, given an initial amount and constant decay rate.

3. Applications of Exponential Decay

Details: Exponential decay models are used in physics (radioactive decay), finance (asset depreciation), biology (drug elimination), and many other fields.

4. Using the Calculator

Tips: Enter initial amount (must be positive), decay rate (between 0 and 1), and time (must be non-negative). All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between exponential decay and growth?
A: Exponential decay decreases over time (r > 0), while growth increases over time (r < 0 in the equivalent growth formula).

Q2: How is half-life related to decay rate?
A: Half-life (t₁/₂) is the time for quantity to reduce by half. It relates to decay rate as: t₁/₂ = ln(2)/λ where λ is the decay constant.

Q3: Can the decay rate be greater than 1?
A: No, in this model the decay rate must be between 0 and 1. Rates >1 would imply negative remaining amounts.

Q4: What units should I use for time?
A: The time units should match the units of your decay rate (e.g., if r is per year, t should be in years).

Q5: How accurate is this model for real-world applications?
A: It works well for systems with constant decay rates, but many real systems have variable rates requiring more complex models.