1. What is the PERT Formula?

The PERT formula calculates exponential growth using the mathematical constant e (approximately 2.71828). It's commonly used in finance, biology, and other fields to model continuous growth processes.

2. How Does the Calculator Work?

The calculator uses the PERT formula:

Where:

• \( v \) — Final value
• \( p \) — Initial value
• \( e \) — Euler's number (~2.71828)
• \( r \) — Growth rate (as decimal)
• \( t \) — Time period

Explanation: The formula calculates continuous compounding growth, where the rate is applied constantly rather than at discrete intervals.

3. Importance of Exponential Growth Calculation

Details: Understanding exponential growth is crucial for financial planning, population studies, and scientific research where quantities grow continuously at a constant rate.

4. Using the Calculator

Tips: Enter initial value in any units, growth rate as decimal (e.g., 0.05 for 5%), and time in appropriate units. All values must be valid (p > 0, t > 0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between PERT and compound interest?
A: PERT models continuous compounding, while standard compound interest compounds at discrete intervals (annually, monthly, etc.).

Q2: What are typical applications of this formula?
A: Population growth, radioactive decay, continuous interest calculations, and biological processes like bacterial growth.

Q3: How do I convert percentage rate to decimal?
A: Divide by 100 (e.g., 5% becomes 0.05).

Q4: What if my growth rate is negative?
A: A negative rate models exponential decay (like radioactive decay or depreciation).

Q5: How accurate is this calculation?
A: Mathematically precise for continuous growth processes, but real-world applications may have additional factors.