Final answer:
If cosmic rays were more intense in the past, there would be a greater initial C-14 concentration in living organisms of that time. This would lead to an overestimation of age in carbon dating, as a higher initial C-14 would take longer to decay to current levels, making the artifact seem older than it actually is.
Step-by-step explanation:
If the number of cosmic rays impacting Earth's atmosphere had been greater in the past than it is now, it would indeed affect our carbon dating estimates of the age of an old ax handle. The crucial assumption in carbon dating is that the cosmic ray intensity has remained constant over time. An increase in cosmic rays in the past would result in a higher production rate of C-14 isotopes, causing living organisms at that time to have more C-14 in their bodies than we would expect.
Upon the death of the organism, the C-14 starts to decay with a half-life of 5,730 years. If archaeologists assume a constant C-14 production rate, they would date an ax handle with increased initial C-14 as being older than it actually is. This is because it would take a longer period for a larger initial amount of C-14 to decay to the level we observe today compared to an object with a standard initial amount of C-14.