1. What is the Exponential Growth/Decay Formula?

The exponential growth/decay formula calculates the final amount after a certain period of time, given an initial amount, growth/decay rate, and time period. It's widely used in finance, biology, physics, and other fields to model processes that change exponentially over time.

2. How Does the Calculator Work?

The calculator uses the exponential growth/decay formula:

Where:

• \( Initial\ Amount \) — Starting value or principal
• \( r \) — Growth/decay rate (as a decimal)
• \( t \) — Time periods

Explanation: The formula calculates how an initial amount grows or decays exponentially over time at a constant rate per period.

3. Applications of Exponential Growth/Decay

Details: This formula is essential for calculating compound interest, population growth, radioactive decay, bacterial growth, and many other natural and financial phenomena that follow exponential patterns.

4. Using the Calculator

Tips: Enter the initial amount, growth/decay rate as a percentage (positive for growth, negative for decay), and time period. All values must be valid numerical inputs.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between growth and decay?
A: Growth occurs when the rate is positive (increasing values), while decay occurs when the rate is negative (decreasing values).

Q2: How is this different from linear growth?
A: Exponential growth compounds over time (growing faster as time passes), while linear growth increases by a fixed amount each period.

Q3: Can this formula handle fractional time periods?
A: Yes, the formula works with any real number for time periods, including fractions.

Q4: What if the rate is 0%?
A: With a 0% rate, the final amount equals the initial amount regardless of time period.

Q5: How does compounding frequency affect the calculation?
A: This formula assumes continuous compounding. For discrete compounding, the formula and inputs would need adjustment.