Exponential Growth

An Exponential Growth is an exponentially increasing function which satisfies an Homogenous First-order Linear Differential Equation.

• Context:
  • It can be expressed as [math]\displaystyle{ x(t)=x_0\;e^{x(t-t_0)} }[/math], where [math]\displaystyle{ N }[/math] satisfies the Homogenous First-order Linear Differential Equation, [math]\displaystyle{ \frac{dN}{dt}=k\; x \quad\textrm{with}\quad x(t_0)=x_0 }[/math].
• Example(s):
  • Moore's Law (for transistors per IC).
  • Exponential Information Technology Growth.
  • …
• Counter-Example(s):
  • Exponential Decay.
  • Linear Growth.
• See: First-Order Linear Differential Equation, Differential Equation, Linear Function.

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