Exponential Decay

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

• Context:
  • It can be expressed as

[math]\displaystyle{ N(t)=N_0\;e^{-\lambda(t-t_0)} }[/math]

where [math]\displaystyle{ N }[/math] satisfies the Homogenous First-order Linear Differential Equation

[math]\displaystyle{ \frac{dN}{dt}=-\lambda N \quad\textrm{with}\quad N(t_0)=N_0 }[/math]

where [math]\displaystyle{ \lambda }[/math] is called the half-life or rate of decay.

• Example(s):
  • …
• Counter-Example(s):
  • Exponential Growth.
• See: First-Order Linear Differential Equation, Differential Equation, Linear Function.

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