Exponential Growth and Decay Calculator
Calculate exponential growth or decay using the formula A = Pe^(rt) for populations, radioactive decay, and compound growth
About this calculator
The Exponential Growth and Decay Calculator uses the formula A = Pe^(rt) to calculate how quantities change exponentially over time. This powerful tool is essential for analyzing population growth, radioactive decay, bacterial cultures, investment compound interest, and carbon dating. Whether you're a student studying exponential functions, a researcher modeling population dynamics, or an investor calculating compound growth, this calculator provides accurate results for any exponential process where the rate of change is proportional to the current amount.
How to use
Enter the initial value (P), growth or decay rate (r as a decimal), and time period (t). For growth, use positive rates; for decay, use negative rates. Click calculate to get the final amount (A). The calculator instantly computes results using the exponential formula A = Pe^(rt).
Frequently asked questions
What's the difference between exponential growth and decay?
Growth uses positive rates (r > 0) where quantities increase over time, while decay uses negative rates (r < 0) where quantities decrease exponentially.
How do I convert percentage rates to decimals?
Divide the percentage by 100. For example, 5% growth becomes 0.05, and 3% decay becomes -0.03 for the rate input.
What does 'e' represent in the formula A = Pe^(rt)?
The letter 'e' is Euler's number (≈2.718), a mathematical constant that naturally describes continuous exponential growth and decay processes in nature and finance.