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 finance, biology, population studies, and many other fields.

2. How Does the Calculator Work?

The calculator uses the exponential growth formula:

Where:

• \( P \) — Future value
• \( P_0 \) — Initial value
• \( r \) — Growth rate per period (as decimal)
• \( n \) — Number of periods

Explanation: The formula calculates compound growth where each period's growth builds on the previous total.

3. Applications of Exponential Growth

Details: This model applies to population growth, compound interest, bacterial growth, radioactive decay (when r is negative), and many natural phenomena.

4. Using the Calculator

Tips: Enter the initial value, growth rate (as decimal - 5% = 0.05), and number of periods. All values must be valid (P₀ ≥ 0, n ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between linear and exponential 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 the growth rate?
A: Divide the percentage by 100 (e.g., 5% becomes 0.05).

Q3: What does negative growth rate mean?
A: A negative growth rate represents exponential decay or reduction over time.

Q4: Can n be a non-integer value?
A: Mathematically yes, but in practice it depends on the context (e.g., for annual growth, n should be whole years).

Q5: What's the rule of 72 in exponential growth?
A: It's a quick way to estimate doubling time: 72 divided by the growth rate percentage gives approximate periods to double.