It is written in Parashat Shemot (Exodus 2:23-24): "And it came to pass in the course of those many days that the king of Egypt died; and the children of Israel sighed by reason of the bondage, and they cried, and their cry came up unto God by reason of the bondage. And God heard their groaning, and God remembered His covenant with Abraham, with Isaac, and with Jacob." In the Midrash (Shemot Rabbah, Parasha 1, Siman 34), these verses are expounded upon regarding the decree on the infants and their rescue. This is the language of the Midrash:

"And it came to pass in the course of those many days"—these were days of sorrow; therefore, they are called 'many'. Similarly, it states: "And if a woman have an issue of her blood many days" (Leviticus 15:25), because they were days of sorrow, they are called 'many'. "And the king of Egypt died"—he became a leper, and a leper is considered as dead, as it is said (Numbers 12:12), "Let her not be as one dead." And it is also said (Isaiah 6:1), "In the year that king Uzziah died." "And the children of Israel sighed"—why did they sigh? Because the magicians of Egypt said: There is no cure for you unless you slaughter 150 of the young children of Israel in the evening and 150 in the morning, and bathe in their blood twice a day. When the Israelites heard of this harsh decree, they began to sigh and lament, and 'they cried out' is an expression of lamentation, as it is written (Ezekiel 21:17), "Cry and wail, son of man." "And their cry came up unto God"—it does not say 'their cry' but 'their cry for help', as it says (Job 24:12), "And the soul of the wounded crieth out for help." "And God heard their groaning"—the groaning of the wounded, as it says (Ezekiel 30:24), "And they shall groan with the groaning of a mortally wounded man." And as it says (Job 24:12), "From out of the city the dying groan." "And God remembered His covenant"—the Israelites were not worthy of being saved, for they were wicked, but they were redeemed by the merit of the Patriarchs. This is what it says, 'And God remembered His covenant.' Our Sages said: A miracle was performed for them, and he (the king of Egypt) was healed from his leprosy. So it is concluded.