Max's vocabulary started exploding around 15-17 months old. I started writing down everything he could say (with understanding of what it means) starting at 18 months, when he could say 107 words. I stopped when he hit 1000 words, a day before his second birthday. During that time, he learned an average of five words a day. Here's the graph:
I did kinda want him to hit 1000, so I spent extra effort teaching him words in the last nine days.
Out of the 1000, he knew 248 Chinese words, 738 English words, and 14 words in other random languages. He learns most of his Chinese words from me, and some at daycare. I speak mostly Chinese to him, but it's not natural for me, so sometimes I switch back to English, plus Chloe speaks all English to him, which is why his English is way ahead.
What kind of words does he know?
(Don't pay too much attention to the long tail of grammar words, I got bored of assigning parts of speech and didn't do it very precisely.)
Among his words, some favorites: contrail, aurora, fluffy, Buddha, skeleton, beige, oval, 面包车, Jupiter, 新年快乐, cuddle, babysitter (pronounced "baby sister"), slime, crunchy, faceplant, and 帅哥.
While I was in the middle of doing this, this image started getting passed around, where a guy tracked the first 100 words his son said.
Funnily enough, in the first 100, it looks exponential, whereas the graph for Max's 100-1000 is pretty linear. Max's graph for 1-100 would have probably looked exponential and very similar to this other kid's but shifted a couple months earlier in age. Well, I'll start from the beginning for the next one!
There's another guy who did this rigorously by actually recording everything in his house for his kid's first three years and then going back to find the first times the kid said each word. From his paper:
Although it is widely known that children’s vocabularies grow more or less exponentially in this developmental period, we found the rate of worth births abruptly drops at 20 months.
Interestingly, Max didn't show this pattern yet–that guy's kid topped out at 3 words per day around 20 months, then dropped way down, only getting to 517 words by age 36 months. I stopped keeping track at 1000, but Max is still learning a ton of new words–not following either trend.
If you want to see the full words, play around with the data, or do a similar vocabulary tracking project of your own, here's the spreadsheet: Max's Vocabulary Words