“exponential decay”的概念、定义、翻译、参考文献-科学参考

exponential decay

Mathematics

If y = Ae^kt, where A>0 and k<0 are constants, and t denotes time, y is said to be exhibiting exponential decay. Then the length of time it takes for y to be reduced to half its value is the same, whatever the value. This length of time, which equals –ln2/k, is called the half‐life and is a useful measure of the rate of decay. It is applicable, for example, to the decay of radioactive isotopes. Compare exponential growth.

Chemical Engineering

The decrease in a quantity at a rate that is proportional to its value:
$\frac{d N}{d t} = - k N$

(p. 136) For example, the decrease in the viability of contaminating microorganisms during the thermal sterilization of foods in the canning process follow this form of decay where the number of surviving microorganisms after time, t, is:
$N = N_{o} e^{- k t}$

where N_o is the initial number and k is the decay constant. The reciprocal of the decay constant is known as the time constant. A special case is the radioactive decay of a substance known as the half-life. This is the time taken for a substance to fall to half of its original value (N = 0.5N_O ):
$t_{1 / 2} = \frac{ln2}{k}$

The half-life of a particular isotope is constant and independent of the amount of starting material.

单词	exponential decay
释义	exponential decay Mathematics If y = Ae^kt, where A>0 and k<0 are constants, and t denotes time, y is said to be exhibiting exponential decay. Then the length of time it takes for y to be reduced to half its value is the same, whatever the value. This length of time, which equals –ln2/k, is called the half‐life and is a useful measure of the rate of decay. It is applicable, for example, to the decay of radioactive isotopes. Compare exponential growth. Chemical Engineering The decrease in a quantity at a rate that is proportional to its value: $\frac{d N}{d t} = - k N$ (p. 136) For example, the decrease in the viability of contaminating microorganisms during the thermal sterilization of foods in the canning process follow this form of decay where the number of surviving microorganisms after time, t, is: $N = N_{o} e^{- k t}$ where N_o is the initial number and k is the decay constant. The reciprocal of the decay constant is known as the time constant. A special case is the radioactive decay of a substance known as the half-life. This is the time taken for a substance to fall to half of its original value (N = 0.5N_O ): $t_{1 / 2} = \frac{ln2}{k}$ The half-life of a particular isotope is constant and independent of the amount of starting material.
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