How do populations change and become extinct?

Sometimes populations overpopulate (get's too large rapidly). Sometimes they get under populated (small amount left). I can give you an example of what would happen if a certain animal, lets say a rabbit, starts to under populate. The predator would be the wolf. Say the ecosystem where the rabbits resided got poisoned and many of the rabbits unfortunately died. The balance got thrown off and now the wolves won't have enough to eat and they'll be scavenging for food more. The rabbits will be in danger of extinction and might get extinct in that ecosystem. I hope I helped! Good luck in your homework.