Exponential Calculator

Calculate exponential functions step by step with explanations and graph analysis.

Enter Exponential Values

Exponential: 2^3

Quick Examples:

About Exponential Functions

What is an Exponential Function?

An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive real number not equal to 1, and x is any real number. The base a determines the growth or decay rate.

Exponential Properties

  1. Product Rule: a^m × a^n = a^(m+n)
  2. Quotient Rule: a^m ÷ a^n = a^(m-n)
  3. Power Rule: (a^m)^n = a^(m×n)
  4. Zero Exponent: a^0 = 1 (for a ≠ 0)
  5. Negative Exponent: a^(-n) = 1/a^n

Applications in Real Life

  • Population growth and decay
  • Compound interest calculations
  • Radioactive decay
  • Bacterial growth
  • Sound intensity and decibels

Frequently Asked Questions

What is the natural exponential function?

The natural exponential function uses base e (approximately 2.718) and is written as e^x or exp(x).

What is the difference between exponential and polynomial growth?

Exponential growth increases at a rate proportional to the current value, while polynomial growth increases at a rate determined by the polynomial degree.