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Half-Life was inspired by the FPS games Doom (1993) and Quake (1996),[12][page needed] Stephen King's 1980 novella The Mist, and a 1963 episode of The Outer Limits titled "The Borderland".[13] According to the designer Harry Teasley, Doom was a major influence and the team wanted Half-Life to "scare you like Doom did". The project had the working title Quiver, after the Arrowhead military base from The Mist.[14] The name Half-Life was chosen because it was evocative of the theme, not clichd, and had a corresponding visual symbol: the Greek letter (lower-case lambda), which represents the decay constant in the half-life equation.[12][page needed] According to the designer Brett Johnson, the level design was inspired by environments in the manga series Akira.[15]

The final portion of the game, taking place in the alien world of Xen, was generally considered the weakest. Besides introducing a wholly new and alien setting, it also featured a number of low-gravity jumping puzzles. The GoldSrc engine did not provide as much precise control for the player during jumping, making these jumps difficult and often with Freeman falling into a void and the player restarting the game.[65][66] Wired's Julie Muncy called the Xen sequence "an abbreviated, unpleasant stop on an alien world with bad platforming and a boss fight against what appeared, by all accounts, to be a giant floating infant".[67] The Electric Playground said that Half-Life was an "immersive and engaging entertainment experience" in its first half and that it "peaked too soon".[68]

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Jeff Lundrigan reviewed the PlayStation 2 version for Next Generation, rating it three out of five, and wrote that "it may be getting old, but there's still a surprising amount of life in Half-Life".[62] The PlayStation 2 version was a nominee for The Electric Playground's 2001 Blister Awards for "Best Console Shooter Game", but lost to Halo: Combat Evolved for Xbox.[72]

After maintaining the 16th place for May in the US,[109] Half-Life exited PC Data's monthly top 20 in June.[110] Half-Life became the fifth-bestselling PC game of the first half of 1999 in the US.[111] Its domestic sales during 1999 reached 290,000 copies by the end of September.[112] During 1999, it was the fifth-best-selling PC game in the US, with sales of 445,123 copies. These sales brought in revenues of $16.6 million, the sixth-highest gross that year for a PC game in the US.[113] The following year, it was the 16th-bestselling PC game in the US, selling another 286,593 copies and earning $8.98 million.[114]

Half-life (symbol t) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.

The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s.[1] Rutherford applied the principle of a radioactive element's half-life in studies of age determination of rocks by measuring the decay period of radium to lead-206.

Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.

A half-life often describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states "half-life is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom, and its half-life is one second, there will not be "half of an atom" left after one second.

Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average". In other words, the probability of a radioactive atom decaying within its half-life is 50%.[2]

For example, the accompanying image is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the process. Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.

The term "half-life" is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below). In a decay process that is not even close to exponential, the half-life will change dramatically while the decay is happening. In this situation it is generally uncommon to talk about half-life in the first place, but sometimes people will describe the decay in terms of its "first half-life", "second half-life", etc., where the first half-life is defined as the time required for decay from the initial value to 50%, the second half-life is from 50% to 25%, and so on.[7]

A biological half-life or elimination half-life is the time it takes for a substance (drug, radioactive nuclide, or other) to lose one-half of its pharmacologic, physiologic, or radiological activity. In a medical context, the half-life may also describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value (the "plasma half-life").

For example, the biological half-life of water in a human being is about 9 to 10 days,[9] though this can be altered by behavior and other conditions. The biological half-life of caesium in human beings is between one and four months.

The concept of a half-life has also been utilized for pesticides in plants,[10] and certain authors maintain that pesticide risk and impact assessment models rely on and are sensitive to information describing dissipation from plants.[11]

In epidemiology, the concept of half-life can refer to the length of time for the number of incident cases in a disease outbreak to drop by half, particularly if the dynamics of the outbreak can be modeled exponentially.[12][13]

Half-life in the context of medical science typically refers to the elimination half-life. The definition of elimination half-life is the length of time required for the concentration of a particular substance (typically a drug) to decrease to half of its starting dose in the body. Understanding the concept of half-life is useful for determining excretion rates as well as steady-state concentrations for any specific drug. Different drugs have different half-lives; however, they all follow this rule: after one half-life has passed, 50% of the initial drug amount is removed from the body. The characteristic decreases of drugs over time have long been studied in a field known as pharmacokinetics and are depictable by basic differential equations. Most clinically relevant drugs tend to follow first-order pharmacokinetics; that is, their drug-elimination rates are proportional to plasma concentrations.[1] In contrast, a few drugs follow zero-order elimination in which the drug amount decreases by a constant amount over time regardless of initial concentration (i.e., ethanol). This article will focus on first-order half-life elimination as it is the most frequently encountered in clinical practice.

Half-life elimination is graphically represented with elimination curves that track the amount of a drug in the body over time, typically with time on the independent axis and drug plasma concentration on the dependent axis, as shown in Figure 1. Total drug exposure over time is represented in these graphs as the integral area under the curve (AUC).[2] Elimination curves are useful for determining if a drug indeed follows first-order kinetics, in which case the curve should follow a logarithmic decay according to the integrated rate law of first-order reactions (Equation 1). After solving the differential equation, one can obtain the half-life equation that is commonly tested on and used in clinical practice (Equation 2). From this equation, one can quickly determine the half-life of a drug, given its predetermined rate constant k. An alternative half-life equation exists that relates half-life to other pharmacokinetic parameters known as the volume of distribution and clearance (Equation 3).[3][4]

It is also worth discussing the relationship between the percentage of drug eliminated and the number of half-lives. Assuming no administration of additional drug after an initial dose, ignoring any drug-drug interactions, and assuming a physiologically healthy individual, certain quantitative constants apply to all drugs exhibiting first-order pharmacokinetics. For example, 90% of a given drug will have undergone elimination after approximately 3.3 half-lives. Even further, 94 to 97% of a drug will have been eliminated after 4 to 5 half-lives. Thus, it follows that after 4 to 5 half-lives, the plasma concentrations of a given drug will be below a clinically relevant concentration and thus will be considered eliminated. Conversely, the accumulation of a drug can reach a steady-state during an infusion. When administering a drug at regular intervals or a constant amount (such as an infusion), the drug achieves a given steady-state concentration after approximately 4 to 5 half-lives without any further accumulation in the body with repeated doses.[5] This state is because the infusion rate and the clearance of the drug will have reached an equilibrium, and thus the net concentration of drug in the body will remain constant. The value of this steady-state concentration is determined by the dosage, dosing interval, and clearance. ff782bc1db