April 21st question

Assume that a certain network can be approximated by a particular continuous model, and its number of nodes increases at a rate given by the function $f(t)=e^{\frac{-t}{1000}+10}$.

Given that at $t=0$, the number of nodes is 0, what is the approximate maximum number of nodes that this network can have? Tip: get an expression for the number of nodes $N(t)$ and its limit when $t\to \mathrm{\infty }$.

1. $e^{\frac{-1}{3}+10}$.
2. $1000e^{\frac{-1}{3}+10}$.
3. $1000e^{10}$.
4. $e^{10}$.
5. None of the above

Original idea by: Christian Konishi