The barrel represents the earth's atmosphere in which the carbon-14 accumulates.
The water leaking out the sides of the barrel represents the loss (mainly by radioactive decay) of the atmosphere's supply of carbon-14.
This argument was popularized by Henry Morris (1974, p.164), who used some calculations done in 1968 by Melvin Cook to get the 10,000-year figure. Whitelaw, using a greater ratio of carbon-14 production to decay, concluded that only 5000 years passed since carbon-14 started forming in the atmosphere!
The argument may be compared to filling a barrel which has numerous small holes in its sides.
The following material has been taken from a sheet entitled Several Faulty Assumptions Are Used in all Radiometric Dating Methods.
Carbon 14 is used for this example:, which was put out by Dr. is presently only 1/3 of the way to an equilibrium value which will be reached in 30,000 years. Knowing how faulty creationist "facts" can be, let's do a little research of our own.
Now, the fuller that barrel gets the more water is going to leak out the thoroughly perforated sides, just as more carbon-14 will decay if you have more of it around.Finally, when the water reaches a certain level in the barrel, the amount of water going into the barrel is equal to the amount leaking out the perforated sides.