I realize this might seem like a very basic question, but I was wondering why the equation is formed as:
3⋅2^n=1536
instead of:
3⋅2^(n−1)=1536
which gives n=10 and is considered incorrect according to the solution video.
My reasoning for using n−1 is that since n includes the first day, the remaining days for doubling would be n−1. However, it seems this logic is incorrect. Am I correct in understanding that my reasoning is wrong only because of the word “after” in the question? If the word “after” wasn’t mentioned, would we then use n−1 as the exponent?
Ah, I see your point. If doubling happens at the end of each day, then at the beginning of the nth day, doubling hasn’t occurred yet. Instead, the doubling will happen at the end of that day, meaning the amount of bacteria on the morning of the (n+1)th day will be the same as the amount at the end of the nth day.
So, we can either:
Assume the starting day is Day 0, or
If we assume the starting day is Day 1, then the bacteria count after the nth day will match the count for the (n+1)th day’s morning.
