Birthrate rhymes with:
administrate, airfreight, arbitrate, calibrate, carbohydrate, castrate, celebrate, concentrate, consecrate, demonstrate, denigrate, disintegrate, emigrate, frustrate, gyrate, hydrate, illustrate, immigrate, infiltrate, integrate, interestrate, magistrate, migrate, narrate, nitrate, orchestrate, penetrate, perpetrate, reintegrate, serrate, substrate, vertebrate
Birthrate sounds like:
bartered, bertrade, bordered, brotherhood