Final answer:
Cats are the species where teeth do not continue to grow, unlike rodents, sharks, and elephants which all have mechanisms for continuous tooth growth or replacement.
Step-by-step explanation:
In the list of species provided, it is cats (Carnivora) that do not have continually growing teeth. Unlike rodents that possess a single pair of continuously growing incisors in both the upper and lower jaws, or elephants which grow a series of molars throughout their life, and sharks that replace their teeth throughout their lifespan, it's the carnivores, such as cats, that have a fixed number of teeth which do not continue to grow once their permanent set has emerged.