指数衰减-Exponential Decay

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Exponential decay is the decrease in a quantity N according to the law
$$N(t)=N_0{e}^{-\lambda t},(1)$$
for a parameter t and constant lambda (known as the decay constant), where $e^x$ is the exponential function and N_{0}=N(0) is the initial value. Exponential decay is common in physical processes such as radioactive decay, cooling in a draft (i.e., by forced convection), and so on. Exponential decay is described by the first-order ordinary differential equation

$$\frac{dN}{dt}=-\lambda N,(2)$$
which can be rearranged to
$$\frac{dN}{N}=-\lambda N,(3)$$
Integrating both sides then gives

$$\ln (\frac{N}{N_0})=-\lambda t,(4)$$
and exponentiating both sides yields the functional form (1).

See https://mathworld.wolfram.com/ExponentialDecay.html

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