1. What is Exponential Decay Factor?

The exponential decay factor represents the fraction of a quantity that remains after a certain time period, given a constant decay rate. It is a fundamental concept in physics, chemistry, biology, and finance for modeling processes that decrease over time.

2. How Does the Calculator Work?

The calculator uses the exponential decay formula:

Where:

• \( e \) — Euler's number (approximately 2.71828)
• \( k \) — Decay rate constant (per unit time)
• \( t \) — Time elapsed

Explanation: The formula calculates the remaining fraction of a substance or quantity after time t, given a decay rate k. The result ranges from 0 to 1, where 1 represents no decay and 0 represents complete decay.

3. Applications of Exponential Decay

Details: Exponential decay is used in radioactive decay calculations, pharmacokinetics (drug elimination), capacitor discharge, population decline models, and depreciation calculations in finance.

4. Using the Calculator

Tips: Enter the decay rate (k) in appropriate units (e.g., per second, per year) and the time (t) in matching time units. Both values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What does the decay factor represent?
A: It represents the fraction of the original quantity that remains after time t. For example, a factor of 0.5 means 50% remains.

Q2: How is decay rate related to half-life?
A: Half-life (t½) = ln(2)/k. The decay rate and half-life are inversely related.

Q3: Can the decay factor be greater than 1?
A: No, since both k and t are non-negative, the factor always ranges from 0 to 1.

Q4: What units should I use for k and t?
A: The units must be consistent. If k is in "per hour", then t should be in hours.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for constant decay rates. Real-world applications may have additional factors to consider.