What is the growth rate of a police officer?

Well, it really depends on your area, department, education and other deciding factors.

Some members of law enforcement later go into politics (including, but not limited to, running for Sheriff). Others may veer toward a specific specialty such as homicide/ arson investigation, drug task force, DUI enforcement, the list goes on.

A lot of members of the federal agencies such as FBI, DEA, INS, Secret Service etc. started out with smaller organizations.,

So really, the potential is there. It's just starting out, learning and finding out specifically what you want to do as a Law Enforcement Officer.