Continuous Exponential Growth Calculator

Uncover the power of continuous growth. Calculate and visualize how quantities increase over time with our intuitive tool.

$

The starting quantity.

%

Annual growth rate (percentage).

Years

Duration over which growth occurs (in years).

Future Value:

The future value after continuous exponential growth is calculated using the formula: $$ FV = PV \cdot e^{(r \cdot t)} $$ where:

  • \( FV \) is the Future Value
  • \( PV \) is the Initial Value (Present Value)
  • \( e \) is Euler's number (approximately 2.71828)
  • \( r \) is the annual growth rate (in decimal form)
  • \( t \) is the time in years

Growth Visualization

Understanding Continuous Exponential Growth

Continuous exponential growth describes how a quantity increases over time when its instantaneous growth rate is proportional to its current value. Unlike discrete growth (e.g., compounded annually), continuous growth happens constantly. It's modeled by the formula $$ FV = PV \cdot e^{(r \cdot t)} $$, where \( e \) is the base of the natural logarithm. This type of growth is prevalent in various real-world scenarios, including population growth, compound interest in finance, and radioactive decay (in reverse, for growth). The key factor is the constant, uninterrupted increase, leading to rapid expansion over time. This calculator helps you explore and understand this powerful mathematical concept.