1. What is Exponential Growth?

Exponential growth describes a process where the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. It's commonly seen in populations, investments, and biological processes.

2. How Does the Calculator Work?

The calculator uses the exponential growth formula:

Where:

• \( P \) — Final value
• \( P_0 \) — Initial value
• \( r \) — Growth rate (as decimal)
• \( t \) — Time period
• \( e \) — Euler's number (~2.71828)

Explanation: The formula calculates how a quantity grows when its growth rate is proportional to its current size.

3. Applications of Exponential Growth

Details: Exponential growth models are used in finance (compound interest), biology (population growth), physics (radioactive decay), and many other fields.

4. Using the Calculator

Tips: Enter the initial value, growth rate (as decimal - 5% = 0.05), 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: Linear growth adds a fixed amount each period, while exponential growth multiplies by a fixed factor each period.

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

Q3: What does 'e' represent in the formula?
A: Euler's number (~2.71828), the base of natural logarithms, representing continuous growth.

Q4: Can this model negative growth?
A: Yes, use a negative growth rate for exponential decay.

Q5: What are limitations of exponential growth models?
A: In reality, growth often slows due to limiting factors (resources, space, etc.).