I know it's hopeless but I have some time to waste:
You need to specify exactly what you are talking about: the atmosphere, an object which might be carbon-dated, or something else.
In the atmosphere:
Decay rate - Production rate = total change rate, and
Production rate = Decay rate (over reasonably short time)
Substituting the second into the first:
Production rate - Production rate = total change rate
But we know Production rate - Production rate = 0, so
0 = total change rate.
In the atmosphere (over reasonably short time) the amount of 14 C does not change.
In an object which is no longer exchanging carbon with the atmosphere (i.e. dead),
Decay rate1 - Production rate1= total change rate1, and
Production rate1 = 0
Substituting the second into the first:
Decay rate1 - 0 = total change rate1
Or
Decay rate1 = total change rate1
[b]The 14C in the object changes] over short periods of time[/b, and changes exponentially via the well-known and established exponential decay.
Originally posted by Omniskeptical
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In the atmosphere:
Decay rate - Production rate = total change rate, and
Production rate = Decay rate (over reasonably short time)
Substituting the second into the first:
Production rate - Production rate = total change rate
But we know Production rate - Production rate = 0, so
0 = total change rate.
In the atmosphere (over reasonably short time) the amount of 14 C does not change.
In an object which is no longer exchanging carbon with the atmosphere (i.e. dead),
Decay rate1 - Production rate1= total change rate1, and
Production rate1 = 0
Substituting the second into the first:
Decay rate1 - 0 = total change rate1
Or
Decay rate1 = total change rate1
[b]The 14C in the object changes] over short periods of time[/b, and changes exponentially via the well-known and established exponential decay.
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