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Topic: Exponential decay

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	Exponential Decay
		Exponential decay models are also used very commonly, especially for radioactive decay, drug concentration in the bloodstream, of depreciation of value.
		Radioactive decay problems are often given in terms of half-life of a radioactive element.
		Write an exponential decay model to find the number of Potassium-40 atoms remaining after t years, if you start with 2000 Potassium-40 atoms.
	hotmath.com /hotmath_help/algebra1/exponential_decay.html (283 words)

	Exponential decay Summary
		Exponential decay is found in mathematical functions where the rate of change is decreasing and thus must reach a limit, which is the horizontal asymptote of an exponential function.
		Exponential decay may also be either decreasing or increasing; the important concept is that it progresses at a slower and slower rate.
		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.
	www.bookrags.com /Exponential_decay (1599 words)

	Science Fair Projects - Exponential decay
		An important characteristic of exponential decay is the time required for the decaying quantity to fall to one half of its initial value.
		In a sample of radionuclides or other particles that undergo radioactive decay to a different state, the number of particles in the original state follows exponential decay.
		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.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Exponential_decay (558 words)

	Exponential decay
		In a sample of radionuclides or other particles that radioactively decay to a different state, the number of particles in the original state follows exponential decay.
		In pharmacology and toxicology, it is found that the body metabolizess many administered substances in an exponential manner.
		The popularity of fashions and other cultural memes (for instance, attendance of popular films) often decays exponentially.
	www.xasa.com /wiki/en/wikipedia/e/ex/exponential_decay.html (367 words)

	4.5 - Exponential and Logarithmic Models
		Exponential decay and be used to model radioactive decay and depreciation.
		Exponential decay models of this form can model sales or learning curves where there is an upper limit.
		Exponential decay models of this form will increase very rapidly at first, and then level off to become asymptotic to the upper limit.
	www.richland.edu /james/lecture/m116/logs/models.html (824 words)

	Exponential decay (Site not responding. Last check: 2007-09-07)
		In mathematics, a quantity that decays exponentially isone that decreases at a rate proportional to its value.
		For example, since a radioactive atom has the same probability to decay at any given time, regardless of how long it alreadylived, the number of disintegrations in an assembly of such atoms is proportional to their number.
		Such an exponentially decayingpopulation decreases, in atom per unit of time, three times as fast when there are six million atoms, as it does when there aretwo millions.
	www.therfcc.org /exponential-decay-15080.html (173 words)

	Course 1, Unit 6 - Exponential Models (Site not responding. Last check: 2007-09-07)
		If b is greater than 1, the pattern will be exponential growth; if b is between 0 and 1, the pattern will be exponential decay.
		represents an exponential growth relationship between x and y, where the initial value of y (when x = 0) is 4, and the y values increase by 30% for each increase of 1 in x values.
		represents an exponential decay relationship between x and y, where the initial value of y (when x = 0) is 4, and the y values decrease by 50% for each increase of 1 in x values.
	www.wmich.edu /cpmp/parentsupport/units/c1u6.html (315 words)

	Exponential decay
		In mathematics, a quantity that decays exponentially is one that decreases at a rate proportional to its value.
		For example, since a radioactive atom has the same probability to decay at any given time, regardless of how long it already lived, the number of disintegrations in an assembly of such atoms is proportional to their number.
		Such an exponentially decaying population decreases, in atom per unit of time, three times as fast when there are six million atoms, as it does when there are two millions.
	www.fact-index.com /e/ex/exponential_decay.html (168 words)

	Radioactive decay and exponential laws
		In his article Light Attenuation and Exponential Laws in the last issue of Plus, Ian Garbett discussed the phenomenon of light attenuation, one of the many physical phenomena in which the exponential function crops up.
		If we have a sample of atoms, and we consider a time interval short enough that the population of atoms hasn't changed significantly through decay, then the proportion of atoms decaying in our short time interval will be proportional to the length of the interval.
		We'll denote the magnitude of the rate of decay of the Carbon 14 nuclei as R.
	www.pass.maths.org /issue14/features/garbett (1244 words)

	Law of radioactive decay (Site not responding. Last check: 2007-09-07)
		The law of radioactive decay predicts how the number of the not decayed nuclei of a given radioactive substance decreases in the course of time.
		In this case a blue point for the time and the fraction of the not yet decayed nuclei is drawn into the diagram.
		For example, even if the probability of a decay within the next second is 99 %, it is nevertheless possible (but improbable) that the nucleus decays after millions of years.
	www.walter-fendt.de /ph14e/lawdecay.htm (280 words)

	APPENDIX D - Exponential Decay (Site not responding. Last check: 2007-09-07)
		Such exponential decay occurs in a wide variety of different physical situations; whenever something changes at a rate proportional to itself.
		Since the probability of decay per nucleus is a constant, the rate of decrease of the nuclei is proportional to the number of nuclei and the result is exponential decay.
		In the discussion of exponential decay, it was convenient to think of the independent variable as time.
	teacher.nsrl.rochester.edu /phy_labs/AppendixD/AppendixD.html (836 words)

	Exponential Growth and Decay
		Exponential growth and decay are rates; that is, they represent the change in some quantity through time.
		Exponential growth is any increase in a quantity (N) -- exponential decay is any decrease in N -- through time according to the equations:
		Exponential growth and decay is a concept that comes up over and over in introductory geoscience: Radioactive decay, population growth, CO increase, etc. When each new topic is introduced, make sure to point out that they have seen this type of function before and should recognize it.
	serc.carleton.edu /quantskills/methods/quantlit/expGandD.html (642 words)

	Exponential Functions
		Exponential functions are characterized by the fact that their rate of growth is proportional to their value.
		with b > 1, and functions governed by exponential decay are of the same form with b < 1.
		Populations might exhibit exponential growth in the absence of constraints, while quantities of a radioactive isotope exhibit exponential decay.
	oregonstate.edu /instruct/mth251/cq/FieldGuide/exponential/lesson.html (310 words)

	The Big Cool Chicken \| Sidebar 1.J
		In the case of conductive, convective and radiant heat transfer, we have seen that the rate of cooling (Q) is very high when the temperature of the object to be cooled is much greater than that of the surroundings and is much lower at temperatures close to those of the surroundings.
		In other words, the decay process occurs most quickly when there are a lot of atoms present. The minus sign is there because parent atoms are decaying into product atoms and so the number of parent atoms is decreasing.
		and so on (any slight discrepancies are just rounding errors). With an exponential decay process, a long time is spent at the tail of the exponential decay curve, where the activity is very low and so a half life is much more useful than the total life.
	www.eng.auburn.edu /%7Ewfgale/usda_course/section1_sidebar_j.htm (525 words)

	Halflife
		The halflife is the amount of time it takes for half of the atoms in a sample to decay.
		In the top picture, you'll see the atoms change color as they decay; the lower picture is a graph showing the number of atoms of each type versus time.
		Notice how the decays are fast and furious at the beginning and slow down over time; you can see this both from the color changes in the top window and from the graph.
	www.colorado.edu /physics/2000/isotopes/radioactive_decay3.html (300 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		The exponential, nonisotropic bounds of Agmon for eigenfunctions corresponding to eigenvalues below the bottom of the essential spectrum are developed, beginning with a discussion of the Agmon metric.
		The analytic method of Combes and Thomas, with improvements due to Barbaroux, Combes, and Hislop, for proving exponential decay of the resolvent, at energies outside of the spectrum of the operator and localized between two disjoint regions, is presented in detail.
		The results are applied to prove the exponential decay of eigenfunctions corresponding to isolated eigenvalues of SchrÃ¶dinger and Dirac operators.
	www.matem.unam.mx /EMIS/journals/EJDE/conf-proc/04/h2/abstr.asc (182 words)

	Math Forum - Ask Dr. Math
		Date: 06/09/2005 at 22:30:14 From: Adam Subject: Exponential Decay Curve of a Radioactive Substance In science we recently had a problem where we had to extend an exponential decay curve of a net counting rate of a radioactive substance by 1 day.
		We had a problem on a test with a radioactive source and an absorptive shield and were supposed to determine the strength of the radiation on the other side of the shield.
		Radiation strength on the other side of a shield, as a function of the thickness of the shield, is an exponential decay function just like radioactive decay.
	www.mathforum.org /library/drmath/view/66823.html (484 words)

	Why Exponentials are Important
		In nature, all linear resonators, such as musical instrument strings and woodwind bores, exhibit exponential decay in their response to a momentary excitation.
		Exponential growth occurs when a quantity is increasing at a rate proportional to the current amount.
		Exponential growth and decay are illustrated in Fig.
	www-ccrma.stanford.edu /~jos/mdft/Why_Exponentials_are_Important.html (321 words)

	Mathwords: Exponential Decay
		A model for decay of a quantity for which the rate of decay is directly proportional to the amount present.
		is a model for exponential decay of 50 grams of a radioactive element that decays at a rate of 1% per year.
		Exponential growth, half-life, continuously compounded interest, logistic growth, e
	www.mathwords.com /e/exponential_decay.htm (111 words)

	Tizzler Decay
		Exponential Decay as a Recurring Theme in Physics
		Given data or a graph, generate the equation of the exponential decay curve
		The curve you drew is an exponential decay curve.
	www.albany.edu /faculty/jae/quarknet/html/tizzler_decay.html (272 words)

	Homework Assignment for Week 2 - PFP 94
		Clearly the number of atoms decaying in one second depends on the number of atoms you start with, but the chance of any individual atom decaying in a given time period is always the same.
		That's exactly the model we need for radioactive decay since the chance of any particular atom decaying in one second is unaffected by the fact that it did not decay a second ago.
		The decays of an isotope of uranium, with a half-life of 4.5 billion years, and of rubidium, with a half-life of 50 billion years, are used to determine the age of rocks found on the surface of the earth and the surface of the moon.
	dept.physics.upenn.edu /courses/gladney/mathphys/hmwrk_week_2.html (3669 words)

	ClickATutor Tutorials
		This law states that a fixed fraction of the element will decay in each unit of time.
		Shown (red dots) is a large number of identical atomic nuclei, each obeying the same decay law.
		Now select the half life time of the nuclei with the slider, press the START button, and watch them decay away as a function of time (displayed in the upper right corner).
	www.clickatutor.com /BasePUB.asp?pid=4730 (222 words)

	Exponential Functions
		Atmospheric pressure as a function of altitude is also represented as an exponential decay function.
		It can be difficult to distinguish graphs of exponential growth from graphs of polynomial growth when the scale is limited.
		Recognizing that numerical values of a function are exponential, as opposed to linear or polynomial or something else, is a difficult task.
	www19.homepage.villanova.edu /alice.deanin/courses/Mat7310/exponential.htm (1553 words)

	2. Graphs of Exponential and Logarithmic Functions
		We saw an example of an exponential growth graph (showing how invested money grows over time) at the beginning of the chapter.
		Exponential growth and decay are common events in science and engineering and it is valuable if you know and recognise the shape of these curves.
		Radioactive decay is the most common example of exponential decay.
	www.intmath.com /Exponential-logarithmic-functions/2_Graphs-exp-log-fns.php (468 words)

	The Law of Exponential Decay (Site not responding. Last check: 2007-09-07)
		The Law of exponential Decay is an application of antiderivatives.
		Both decay and growth are included in the theorem below.
		C is the initial value of y, and k is the proportionality constant.
	library.thinkquest.org /3616/Calc/S3/TLoED.html (269 words)

	One phase exponential decay (Site not responding. Last check: 2007-09-07)
		This equation describes the kinetics such as the decay of radioactive isotopes, the elimination of drugs, and the dissociation of a ligand from a receptor.
		Y starts out equal to SPAN+PLATEAU and decreases to PLATEAU with a rate constant K. The half-life of the decay is 0.6932/K. SPAN and PLATEAU are expressed in the same units as the Y axis.
		When fitting data to this equation, consider fixing the plateau to a constant value of zero.
	www.graphpad.com /curvefit/id204.htm (101 words)

	Exponentials
		The exponential function is by far the most important function in all of mathematics (this becomes especially true when one considers generalizations of exponential functions from real to complex numbers and beyond to more exotic situations).
		For an example of exponential decay, consider the process by which kerosene is purified to make jet fuel - pollutants are removed by passing the kerosene through a special clay filter.
		Another standard measure of the relative speed with which an exponential function grows (or decays) is to give the length of the interval on the x axis that it takes for the value of y to exactly double (or divide in half).
	dept.physics.upenn.edu /courses/gladney/mathphys/subsubsection1_1_4_1.html (818 words)

	Exponential decay law
		It was shown very early on that decay is a random process: this gives rise to an exponential decay law.
		The decay of (a particular state of) a nucleus is determined by one number, the decay constant
		The probability is thus independent of time, it is independent of the age of a particular nucleus and is the same for all nuclei in the same state (i.e.
	www.phy.uct.ac.za /courses/phy300w/np/ch1/node30.html (442 words)

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