What will happen to a population of predators if there is a sudden increased in food for the prey

A sudden increase in food would result in prey eating and breeding which would mean more the predators could do the same. The predator population would increase with the population of its prey.

At first, the population of predators would spike and increase quickly, but then over time, gradually decrease.

(This is because at first there's more food, so the predators population increases. But overtime it begins to level out and the predators' population catches up with the prey, and in result, doesn't continue increasing.)