Exponential Decay Systems that exhibit exponential decay behave according to the model 6817 y y 0 e k t where y 0 represents the initial state of the system and k 0 is a constant called the decay constant. Any exponential function can be written in the form mathbfy aekx mathbfk is called the continuous growth or decay rate. The coefficient k plays the role of the rate of growth similarly as r does in the original exponential growth formula.
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Symbolically this process can be expressed by the following differential equation where N is the quantity and l lambda is a positive rate called the exponential decay constant. P 0 initial amount at time t 0. Exponential decay is the change that occurs when an original amount is reduced by a consistent rate over a period of time. The model is nearly the same except there is a negative sign in the exponent.