HALF-LIFE sends a shock through the game industry with its combination of pounding action and continuous, immersive storytelling. Valve's debut title wins more than 50 game-of-the-year awards on its way to being named 'Best PC Game Ever' by PC Gamer, and launches a franchise with more than eight million retail units sold worldwide. Half-Life 2, stylized as HλLF-LIFE 2, is a science fiction first-person shooter developed and published by Valve Corporation, and released on November 16, 2004, following an extended development period of five years. The game garnered near unanimous positive reviews and received critical acclaim, winning over 50 Game of the Year awards.
Rewrite the function in terms of half-life.
Of course, our function does not depend on generic variable x,{displaystyle x,} but time t.{displaystyle t.}
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- f(t)=(12)t{displaystyle f(t)=left({frac {1}{2}}right)^{t}}
- Simply replacing the variable doesn't tell us everything, though. We still have to account for the actual half-life, which is, for our purposes, a constant.
- We could then add the half-life t1/2{displaystyle t_{1/2}} into the exponent, but we need to be careful about how we do this. Another property of exponential functions in physics is that the exponent must be dimensionless. Since we know that the amount of substance depends on time, we must then divide by the half-life, which is measured in units of time as well, to obtain a dimensionless quantity.
- Doing so also implies that t1/2{displaystyle t_{1/2}} and t{displaystyle t} be measured in the same units as well. As such, we obtain the function below.
- f(t)=(12)tt1/2{displaystyle f(t)=left({frac {1}{2}}right)^{frac {t}{t_{1/2}}}}