It’s the yeast/bacterial colony that is 100 years old, not the individual yeast/bacteria organisms.
Imagine you start with 1000 microbes (it would be much more than this, but just for simplicity). Each time you make bread, you use 900 of them in the recipe. Those 900 all die in that process when you bake the bread. You feed the remaining 100 some flour and water and this allows them to reproduce back up to 1000 before you make bread again and repeat the process.
So the colony lives on, but you’re regularly killing most of the population and then helping it repopulate.
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