Derivative Word Problem about Virus Spreading

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I had this question on a practice sheet for our calculus unit, and I am kind of confused by the following question. At lunch one day, the flu rapidly starts infecting the students at the school. Assuming that every kid in the school eventually catches the flu, which can be modeled by f(t) = $\frac{1000}{1+19e^{-t}}$, where f(t) is the number of people who have had the flu, and t is the number of days. The question asked how many students are at the school, which I didn't get how to solve, apparently the answer is 1000, but I am not sure exactly as to why (I obviously see the fact that 1000 is in the numerator, but I don't know why it translates to being the answer).

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Consider the limit as t approaches infinity of f(t). If the disease is allowed to spread for an infinite amount of time, then everyone in the school will catch it.