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# What is the difference between exponential and nonexponential decay?

Updated: 12/10/2022

Wiki User

14y ago

Perhaps a good way to explain the difference between exponential and nonexponential decay (like perhaps linear decay) would be to use some examples. In radioactive decay, which is exponential decay, the rate of decay is a function of the amount of material present. The more you have to start with, the more decays per unit of time. The less you begin with the smaller that number of decay events in a given period. And as the decay continues the number of decay events per unit of time decreases. (A consequence is that the material might never be seen to all "go away" in time.) Radioactive decay is a function of the amount of material undergoing decay, and the rate of decay is exponential. That is, when we write the equations for the phenomenon, we'll be using exponents in the expressions to account for the dependence of the decay rate on the amount of material present. There is a good comparison to this. Let's say a group of students is in a classroom and leaves at the bell. The all get up and hit the door, but the rate at which the students can get out is basically a function of the width of the doorway, and not how many students are trying to get out. This is easy to see. If the students go through the door at one student per second and 30 students were in the class, it will take 30 seconds for them to all leave. The rate of "decay" of the population in the room is constant at one student per second. It does not change. It was the same when all the students were trying to get out, and remains constant even as the last couple of students are trying to exit. It is a nonexponential "decay" scheme, and is, in fact, a linear one. The equation expressing the egress phenomenon will not have any exponents in it; all the terms will be what are called first order terms. No "powers" of a number or variable will appear. (A consequence is that the room will empty of students, and definitely so. This is a contrast to radioactive decay.)

Wiki User

14y ago