Exponential decay

A <a href="/facts/Quantity/E2jCKetq">quantity</a> is subject to exponential decay if it decreases at a rate <a href="/facts/Proportionality_(mathematics)/xDQmfh6t">proportional</a> to its current value. Symbolically, this process can be expressed by the following <a href="/facts/Differential_equation/9MGbE3Ca">differential equation</a>, where N is the quantity and λ (<a href="/facts/Lambda/ykr3WSse">lambda</a>) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant:

d
              N
              (
              t
              )
            
            
              d
              t
            
          
        
        =
        −
        λ
        N
        (
        t
        )
        .
      
    
    {\displaystyle {\frac {dN(t)}{dt}}=-\lambda N(t).}

The solution to this equation (see derivation below) is:

N
        (
        t
        )
        =
        
          N
          
            0
          
        
        
          e
          
            −
            λ
            t
          
        
        ,
      
    
    {\displaystyle N(t)=N_{0}e^{-\lambda t},}

where N(t) is the quantity at time t, N0 = N(0) is the initial quantity, that is, the quantity at time t = 0.

Exponential decay open-in-new

Exponential decay