Editing Exponential decay (section)

=== Natural sciences ===<!-- This section is linked from [[Methicillin-resistant Staphylococcus aureus]] -->
* '''[[Chemical reactions]]:''' The [[reaction rate|rate]]s of certain types of [[chemical reaction]]s depend on the concentration of one or another [[reactant]]. Reactions whose rate depends only on the concentration of one reactant (known as [[Rate equation#First-order reactions|first-order reactions]]) consequently follow exponential decay. For instance, many [[enzyme]]-[[catalysis|catalyzed]] reactions behave this way.
* '''[[Electrostatics]]:''' In a [[RC circuit]], the [[electric charge]] (or, equivalently, the [[electric potential|potential]]) contained in a [[capacitor]] (capacitance ''C'') discharges through a constant [[External electric load|external load]] (resistance ''R'') with exponential decay and similarly charges with the [[mirror image]] of exponential decay (when the capacitor is charged from a constant voltage source though a constant resistance). The exponential time-constant for the process is <math>\tau = R \, C ,</math> so the half-life is <math>R \, C \, \ln(2) .</math> The same equations can be applied to [[Duality (electrical circuits)|the dual]] of current in an inductor.
** Furthermore, the particular case of a capacitor or inductor changing through several [[Series and parallel circuits#Parallel circuits|parallel]] [[resistor]]s makes an interesting example of multiple decay processes, with each resistor representing a separate process. In fact, the expression for the [[resistor#Series and parallel circuits|equivalent resistance]] of two resistors in parallel mirrors the equation for the half-life with two decay processes.
* '''[[Geophysics]]:''' [[Atmospheric pressure]] decreases approximately exponentially with increasing height above sea level, at a rate of about 12% per 1000m.{{citation needed|date=November 2017}}
* '''[[Heat transfer]]:''' If an object at one [[temperature]] is exposed to a medium of another temperature, the temperature difference between the object and the medium follows exponential decay (in the limit of slow processes; equivalent to "good" heat conduction inside the object, so that its temperature remains relatively uniform through its volume).  See also [[Newton's law of cooling]].
* '''[[Luminescence]]:''' After excitation, the emission intensity – which is proportional to the number of excited atoms or molecules – of a luminescent material decays exponentially. Depending on the number of mechanisms involved, the decay can be mono- or multi-exponential.
* '''[[Pharmacology]] and [[toxicology]]:''' It is found that many administered substances are distributed and [[metabolism|metabolize]]d (see ''[[clearance (medicine)|clearance]]'') according to exponential decay patterns.  The [[biological half-life|biological half-lives]] "alpha half-life" and "beta half-life" of a substance measure how quickly a substance is distributed and eliminated.
* '''[[Physical optics]]:''' The intensity of [[electromagnetic radiation]] such as light or X-rays or gamma rays in an absorbent medium, follows an exponential decrease with distance into the absorbing medium.  This is known as the [[Beer-Lambert]] law.
* '''[[Radioactivity]]:''' In a sample of a [[radionuclide]] that undergoes [[radioactive decay]] to a different state, the number of atoms in the original state follows exponential decay as long as the remaining number of atoms is large. The decay product is termed a [[radiogenic]] nuclide.
* '''[[Thermoelectricity]]:''' The decline in resistance of a Negative Temperature Coefficient [[Thermistor]] as temperature is increased.
* '''[[Vibrations]]:''' Some vibrations may decay exponentially; this characteristic is often found in [[Harmonic oscillator|damped mechanical oscillators]], and used in creating [[ADSR envelope]]s in [[Synthesizer#Sound basics|synthesizers]].  An [[overdamped]] system will simply return to equilibrium via an exponential decay.
* '''Beer froth:''' Arnd Leike, of the [[Ludwig Maximilian University of Munich]], won an [[List of Ig Nobel Prize winners|Ig Nobel Prize]] for demonstrating that [[beer]] froth obeys the law of exponential decay.<ref>{{Cite journal| last1 = Leike | first1 = A.| title = Demonstration of the exponential decay law using beer froth| journal = European Journal of Physics| volume = 23| pages = 21–26| year = 2002| issue = 1| doi = 10.1088/0143-0807/23/1/304|bibcode = 2002EJPh...23...21L | citeseerx = 10.1.1.693.5948| s2cid = 250873501}}</ref>