Debug Info:
{
  "title": "Exponential Function",
  "symbol": "e^x",
  "definition": "The exponential function is a mathematical function that quickly grows in value as its input increases. It is commonly written as e^x, where e is Euler's number.",
  "usage": "Used in modeling growth and decay processes, compound interest, and many natural phenomena.",
  "examples": [
    {
      "description": "Basic form",
      "latex": "f(x) = e^x"
    },
    {
      "description": "General form",
      "latex": "f(x) = a \\cdot e^{bx}"
    }
  ],
  "tags": [
    "calculus",
    "analysis",
    "functions"
  ],
  "relatedConcepts": [
    "natural logarithm",
    "derivative",
    "Taylor series"
  ]
}

Exponential Function

Symbol

e^x

Definition

The exponential function is a mathematical function that quickly grows in value as its input increases. It is commonly written as e^x, where e is Euler's number.

Usage

Used in modeling growth and decay processes, compound interest, and many natural phenomena.

Examples

Description: Basic form

LaTeX: f(x) = e^x
Description: General form

LaTeX: f(x) = a \cdot e^{bx}

Tags