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.
To that end, he quoted some authorities, including Richard Lingenfelter.
Having accomplished that, Morris concluded that the barrel was still in the process of being filled up and that, given the present rate of water coming in and leaking out, the filling process began only 10,000 years ago.
That is, the equilibrium point should have long since been reached given the present rate of carbon-14 production and the old age of the earth.
The next step in Henry Morris' argument was to show that the water level in our barrel analogy was not in equilibrium, that considerably more water was coming in than leaking out.
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!