1. What is the Growth/Decay Formula?

The growth/decay formula calculates how a quantity changes over time when it grows or decays at a constant rate. It's widely used in finance, biology, physics, and other fields to model exponential changes.

2. How Does the Calculator Work?

The calculator uses the growth/decay formula:

Where:

• \( Initial \) — Starting value
• \( r \) — Growth rate (positive) or decay rate (negative) as decimal
• \( t \) — Number of time periods
• \( Value \) — Result after time t

Explanation: The formula shows exponential growth when r > 0 and exponential decay when r < 0. The rate compounds over each time period.

3. Importance of Growth/Decay Calculation

Details: This calculation is essential for understanding compound interest, population growth, radioactive decay, and many other natural and financial processes that change exponentially over time.

4. Using the Calculator

Tips: Enter the initial value, rate as decimal (e.g., 0.05 for 5%), and time periods. For decay, use negative rate (e.g., -0.03 for 3% decay).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between growth and decay?
A: Growth increases the value over time (positive rate), while decay decreases it (negative rate).

Q2: How is this different from linear growth?
A: Exponential growth compounds on previous growth, leading to faster increase than linear (constant amount per period).

Q3: What are common applications?
A: Compound interest calculations, population modeling, radioactive decay, bacterial growth, and investment analysis.

Q4: How do I convert percentage to decimal?
A: Divide percentage by 100 (e.g., 5% = 0.05, -2% = -0.02).

Q5: What if time isn't whole numbers?
A: The formula works for fractional time periods, useful for continuous processes.