exponentially — at an increasingly rapid rate; in a way that becomes progressively faster

a farm worker looks amazed as he counts rabbit families that have multiplied dramatically. What started as two rabbits in the first pen has become four in the second pen. The third pen shows eight rabbits hopping around energetically. The fourth pen contains sixteen rabbits of various sizes crowding the space. The final pen overflows with thirty-two rabbits as some hop over the fence. Other farm workers rush over with additional food and larger enclosures to handle the overwhelming growth. growth happening at an increasingly rapid rate in a way that becomes progressively faster