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It depends highly on the mechanism of carcinogenesis. Lead is a (possible) carcinogen, and accumulates even in relatively small quantities because it takes up residence in your bones and is slowly released back into your blood over years. Others may be eliminated rapidly and only cause damage in large or continuous doses. Frustratingly the answer is often "it depends". The very low end of the spectrum of exposures is often the most relevant to humans (due to our relatively low exposure to most things), but very hard to study, because the effects are often drowned out by other causes of morbidity/mortality.

In a side note, Organophosphates replaced Organochlorides for a very similar reason. They have a much faster elimination rate, reducing the time that they stay in the food chain (and hopefully reducing the exposure of non-target species). Organochlorines, on the other hand, were very stable, which made them easily stored, but also caused biomagnification, where animals further up the food chain started concentrating it in their bodies as they ate smaller animals that had been exposed. This caused serious environmental effects, leading to the shift to the pesticides we use today.