Why does it make sense in this situation that the function has this horizontal asymptote?

If each person’s vacation costs $630 plus a fixed tour-guide fee shared by the group, the average cost is $630 plus the guide fee divided by the number of people. That extra amount stays positive, so the average is always greater than $630, but it gets smaller as more people join. The average cost therefore approaches the horizontal asymptote of $630 without reaching it.

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