1. What is the PERT Formula?

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

2. How Does the Calculator Work?

The calculator uses the PERT formula:

Where:

• \( A \) — Final amount (units)
• \( P \) — Initial amount (units)
• \( e \) — Euler's number (~2.718)
• \( r \) — Growth rate (decimal)
• \( t \) — Time period (units)

Explanation: The formula calculates the continuous compounding effect where growth happens constantly rather than at discrete intervals.

3. Importance of Continuous Growth Calculation

Details: Continuous growth models are essential for accurate predictions in financial investments, population studies, radioactive decay, and other natural processes where change occurs continuously.

4. Using the Calculator

Tips: Enter initial value (P) in units, growth rate (r) as decimal (e.g., 0.05 for 5%), and time (t) in 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 formulas assume discrete compounding periods (yearly, quarterly, etc.).

Q2: Can this be used for decay calculations?
A: Yes, use a negative growth rate for decay scenarios (e.g., radioactive decay).

Q3: What are common applications of this formula?
A: Population growth, investment growth, bacterial growth, radioactive decay, and temperature change modeling.

Q4: How precise is this calculation?
A: Extremely precise for continuous processes. For discrete processes, standard compound formulas may be more appropriate.

Q5: What units should I use for time?
A: The time units must match the rate units (e.g., if rate is per year, time should be in years).