Not as fast as we used to. A friend of mine, who went to college at MIT around 1980, had a classmate who was the son of an undertaker. His dad had told him that when he (the dad) had entered the business, you had to work fast. Bodies would start to smell quickly. But now — around 1980 — that was no longer necessary. You could wait a lot longer before they smelled bad.
Which I take to mean that around 1980 the average old person, where this classmate came from, had a lot less bacteria in their body than around 1960. All that concern about "the safety of the food supply" — preservatives, yes, but also sterilization, freezing, sell-by dates, food handling rules, food safety officers, and microwave food — seems to have had an effect. From 1960 to 1980 there was a big shift from homemade food to factory-made and restaurant-made food. The uniformity of the new food caused the obesity epidemic, I believe; its sterility caused a great increase in allergies and asthma, not to mention a bunch of other disorders.
Speaking of sell-by dates, at a Japanese grocery store recently I wanted to buy some Yakult. At check-out, it was pointed out to me that it was one day past its sell-by date. Half price. I bought two.