📈 Exponential Graph Plotter
📌 Understanding Exponential Graphs
An exponential graph represents rapid growth or decay and follows the function:
y = a * e^(bx)
- **X-Axis Values:** Represent input values for exponential calculations.
- **Y-Axis Values:** Represent exponentially transformed values.
📌 Examples of Exponential Graphs
| X Values | Exp(X) Values |
|---|---|
| 1, 2, 3, 4 | 2.7, 7.4, 20.1, 54.6 |
| -2, -1, 0, 1, 2 | 0.14, 0.37, 1, 2.71, 7.39 |
| 5, 6, 7, 8 | 148.4, 403.4, 1096.6, 2980.9 |
🔧 Practical Applications of Exponential Graphs
1. Population Growth: Used to model human and bacterial population growth over time.
2. Finance & Economics: Represents compound interest, investment growth, and inflation trends.
3. Physics & Engineering: Describes radioactive decay, electrical circuits, and energy dissipation.
❓ FAQs
Q1: How do I generate an exponential graph?
✅ Enter comma-separated X values, then click “Generate Exponential Graph” to visualize the rapid growth pattern.
Q2: What are exponential graphs used for?
✅ Exponential graphs are used in finance, science, and engineering to model growth and decay.
Q3: Can exponential graphs show negative values?
✅ Yes, but the function’s growth behavior changes for negative values depending on the exponent.
Q4: How do I interpret an exponential graph?
✅ Exponential graphs show steep increases or decreases, often indicating rapid change.
Q5: Where are exponential graphs commonly used?
✅ They are widely used in epidemiology, physics, economics, and environmental science.