The simplest way to answer this is to look at the total XP, not the XP to next level.

From each level, the XP required to reach the next level looks like this:

(this graph borrowed from Dale M's answer)

This doesn't make a lot of sense, which is the source of the confusion. However, if you look at a character's total XP as they progress through the levels, it looks like this:

This nice smooth curve makes it much more obvious. The slight deviations from the curve are because each level has been rounded to the nearest multiple of 1000 (or 5000 at higher levels). That rounding is likely the source of the strange progression in XP-to-next-level, and the fact that the curve flattens tends to a rough asymptote explains the flattening off of the increases in XP-to-next-level. From this graph, the XP required to level up is simply (next - current), and at that point the slight wobbles in the curve are made much more obvious.

The simplest way to answer this is to look at the total XP, not the XP to next level.

From each level, the XP required to reach the next level looks like this:

(this graph borrowed from Dale M's answer)

This doesn't make a lot of sense, which is the source of the confusion. However, if you look at a character's total XP as they progress through the levels, it looks like this:

This nice smooth curve makes it much more obvious. The slight deviations from the curve are because each level has been rounded to the nearest multiple of 1000 (or 5000 at higher levels). That rounding is likely the source of the strange progression in XP-to-next-level, and the fact that the curve flattens tends to a rough asymptote explains the flattening off of the increases in XP-to-next-level. From this graph, the XP required to level up is simply (next - current), and at that point the slight wobbles in the curve are made much more obvious.