How long will cooked olive oil (used to roast long hots and garlic) last as a condiment?

Let's say I've roasted some long hot peppers and garlic in a 400° oven for 10 minutes. I'm going to use everything on a roast pork sandwich but I've got some of the oil left over. I'd like to save this just to drizzle on sandwiches and salads.

How long should the oil last either at room temp or in the fridge?

Bonus question; what's the science that would answer this question for me? Or rather, if roasted olive oil I will last at room temp for 10 days, why 10 instead of 5 or 15?

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