Since frogs are ectotherms and supposed to have low metabolic rate, why do they grow so fast and eat so much?
Rather than saying ectotherms can't grow fast (which is obviously false), it's probably better to think about it as a two-part argument:


Ectotherms and endotherms can grow rapidly at an optimum temperature
Ectotherms can't maintain themselves at their optimum growth temperature


If you keep ectotherms at their optimum temperature, then they can reach optimum growth. In the wild, they might not find that optimum temperature for more than a few hours per day, though in your aquarium they might be at it all day long. 

There are several publications supporting this such as 


Effects of temperature and volume of water on the growth and development of tadpoles of Pleurodema diplolister and Rhinella granulosa (Amphibia: Anura)
Effects of Temperature on Growth, Development and Survival in Larvae of Pelophylax ridibundus (Pallas, 1771) (Amphibia: Anura): Linking Global Warming to Amphibian Development
Thermal tolerance limits and effects of temperature on the growth and development of the green toad, Bufotes viridis


I don't see a specific reference for this but will add that ectotherm probably have greater growth potential than endotherms if they're at their optimum temperature, because endotherms have to waste energy on a whole suite of molecular machinery that's designed to maintain their body temperature.  All that extra energy can be diverted into growth by ectotherms.