See the attached graphic. (I'm rewording the attached formula)
Ending amount = Beginning Amount * e ^(k * t)
where "e" is the mathematical constant 2.718281828
and k = natural log (.5) / half-life
k = -.693147 / 5,730 = <span><span><span>-0.000120968062827225 </span> </span> </span>
Ending amount = 52 * e ^(-0.000120968062827225* t)
As a test, let's see how much remains after <span> <span> <span> 11,460 </span> years.</span>
</span>Ending amount = 52 * e ^(-0.000120968062827225 * 11,460)
Ending amount = 52 * e ^ ( <span> <span> <span> -1.386294 </span> </span> </span> )
Ending amount = 52 * <span> <span> <span> 0.250000
</span></span></span>Ending amount = 13
(which is correct because that is one quarter of the amount after two half-lives).
Source:
http://www.1728.org/halflif2.htm
Ending amount = Beginning Amount * e ^(k * t)
where "e" is the mathematical constant 2.718281828
and k = natural log (.5) / half-life
k = -.693147 / 5,730 = <span><span><span>-0.000120968062827225 </span> </span> </span>
Ending amount = 52 * e ^(-0.000120968062827225* t)
As a test, let's see how much remains after <span> <span> <span> 11,460 </span> years.</span>
</span>Ending amount = 52 * e ^(-0.000120968062827225 * 11,460)
Ending amount = 52 * e ^ ( <span> <span> <span> -1.386294 </span> </span> </span> )
Ending amount = 52 * <span> <span> <span> 0.250000
</span></span></span>Ending amount = 13
(which is correct because that is one quarter of the amount after two half-lives).
Source:
http://www.1728.org/halflif2.htm