1. What is the Exponential Growth Formula?

The exponential growth formula describes how quantities increase over time when the growth rate is proportional to the current size. It's widely used in population studies, finance, physics, and many other fields.

2. How Does the Calculator Work?

The calculator uses the exponential growth formula:

Where:

• \( N \) — Final value
• \( N_0 \) — Initial value
• \( r \) — Growth rate (per time unit)
• \( t \) — Time elapsed
• \( e \) — Euler's number (~2.71828)

Explanation: The formula shows how a quantity grows exponentially when the growth rate is constant relative to the current size.

3. Importance of Exponential Growth Calculation

Details: Understanding exponential growth is crucial for predicting population growth, investment returns, bacterial growth, and many natural phenomena where growth compounds continuously.

4. Using the Calculator

Tips: Enter the initial value, growth rate (as a decimal, e.g., 0.05 for 5%), and time period. All values must be valid (initial value > 0, time ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between exponential and linear growth?
A: Exponential growth increases by a percentage of the current value, while linear growth adds a fixed amount each period.

Q2: How do I convert percentage growth rate to decimal?
A: Divide the percentage by 100 (e.g., 5% becomes 0.05).

Q3: What does negative growth rate mean?
A: A negative rate represents exponential decay rather than growth.

Q4: When is exponential growth model appropriate?
A: When growth depends on current size and resources are unlimited (early stages of population growth, compound interest, etc.).

Q5: What are limitations of this model?
A: Real systems often face resource limits that eventually slow growth (logistic growth models account for this).