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Exponential Decay - Math Central
In real-world applications, we need to model the behavior of a function. In mathematical modeling, we choose a familiar general function with properties that suggest that it will model the real-world phenomenon we wish to analyze. In the case of rapid growth, we may choose the exponential growth function:. We may use the exponential growth function in applications involving doubling time , the time it takes for a quantity to double.
Introduction to exponential decay
Right now, 40, feet overhead, a cosmic ray is sending a neutron smashing into a nitrogen atom, smacking a proton out of its nucleus and forming an isotope called carbon Living things constantly consume carbon—through photosynthesis, for plants, and for animals, ingestion of those plants. The atmospheric ratio of carbon to regular carbon remains consistent at one part per trillion, so if something is alive, one-trillionth of its carbon atoms will be C But once a plant or animal dies, its carbon is no longer replenished. C is radioactive and unstable, with a half-life of 5, years, which means that half the atoms will turn back into nitrogen over that period.
Exponential decay is a particular form of a very rapid decrease in some quantity. One specific example of exponential decay is purified kerosene, used for jet fuel. The kerosene is purified by removing pollutants, using a clay filter. If P o is the initial amount of pollutants in the kerosene, then the amount left, P , after n feet of pipe can be represented by the following equation:.