1. What is Exponential Growth/Decay?

Exponential growth occurs when the growth rate of a value is proportional to its current value, resulting in increasingly rapid growth over time. Exponential decay follows the same principle but with a negative growth rate, leading to decreasing values.

2. How Does the Calculator Work?

The calculator uses the exponential growth/decay formula:

Where:

• \( y \) — Final value
• \( y_0 \) — Initial value
• \( r \) — Growth/decay rate (as decimal)
• \( t \) — Number of time periods

Explanation: The formula calculates how a quantity changes over time when the change is proportional to the current amount.

3. Applications of Exponential Growth/Decay

Details: This model is used in population growth, radioactive decay, compound interest, viral spread, and many other natural and financial phenomena.

4. Using the Calculator

Tips: Enter the initial value, growth/decay rate (positive for growth, negative for decay), and number of time periods. All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between growth and decay?
A: Growth occurs when r is positive (values increase), decay when r is negative (values decrease).

Q2: How is this different from linear growth?
A: Linear growth adds a fixed amount each period, while exponential growth multiplies by a fixed factor.

Q3: What are common examples of exponential growth?
A: Population growth, compound interest, and viral spread are classic examples.

Q4: What are common examples of exponential decay?
A: Radioactive decay, cooling of objects, and drug elimination from the body.

Q5: How do I calculate doubling time?
A: For growth, doubling time ≈ 70 divided by the percentage growth rate (rule of 70).