It's always difficult to provide server specification based on user population but 2 CPU cores and 2 GB RAM sounds inadequate for 13,000 users. I would have thought that 100 users accessing the site simultaneously (e.g. near an assignment deadline) would cause the site to run extremely slowly.
If possible increase this to 4 or 6 CPUs, and 8 GB or 16 GB of RAM. Remember the server has to handle user requests and (presumably) is your database server too.
Depending on the usage patterns (i.e. how many people will be using the site at a single time and the kind of activities they will be performing) this specification may need to be improved further.
In short: you can't really use a free plan to provide a service to 10,000+ users.