Growth or Decay Rate Calculator
Understanding Exponential Growth and Decay
Exponential growth and decay are mathematical concepts used to describe how quantities change over time when the rate of change is proportional to the current amount. This calculator helps you determine the percentage rate of change per unit of time based on the initial and final values provided.
The Mathematical Formula
This calculator uses the standard growth/decay formula to solve for the rate (r):
- N₀: The initial amount at the start of the period.
- Nₜ: The final amount after the time has elapsed.
- t: The number of time intervals (days, years, hours, etc.).
- r: The percentage growth or decay rate.
Real-World Examples
1. Population Growth: If a town starts with 50,000 residents and grows to 65,000 over 10 years, what is the annual growth rate? Using the calculator, we find a steady annual increase of 2.66%.
2. Radioactive Decay: If a sample of a radioactive isotope goes from 500mg to 400mg over 4 days, it is decaying. The calculator will show a negative result, indicating a decay rate of -5.43% per day.
3. Investment Performance: While not a loan, you can use this to see the compounded growth of an asset. If an investment goes from 1,000 to 1,800 over 8 years, you are looking at a 7.62% compound annual growth rate (CAGR).
How to Interpret the Results
If the Final Quantity is larger than the Initial Quantity, the result will be positive, indicating Growth. If the Final Quantity is smaller, the result will be negative, indicating Decay.