It's a great argument except for one, little thing.
The water is coming out of the hose at a steady rate as our model assumed!
Charles Darwin strongly promoted the idea that life was generated spontaneously from non-life.
However, Louis Pasteur, a French microbiologist and believer in biblical creation, made a startling discovery that turned this notion completely upside down.
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.
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.We stick the garden hose in and turn it on full blast.The water coming out of the hose is analogous to the continuous production of carbon-14 atoms in the upper atmosphere.(Strahler, 1987, p.158) Lingenfelter actually attributed the discrepancy between the production and decay rates to possible variations in the earth's magnetic field, a conclusion which would have ruined Morris's argument.Henry Morris chose not to mention that portion of the paper!The barrel represents the earth's atmosphere in which the carbon-14 accumulates.