After data were collected during an experiment, it was concluded that a population of bacteria could be modeled by the equation $P(t)=k{a}^2,$ where $k$ and a are positive constants and $t$ is the time, in hours, after the beginning of the experiment. According to the model, the population at $4$ hours and at $6$ hours after the beginning of the experiment was $4000$ and $16,000,$ respectively. Approximately what was the number of bacteria at the beginning of the experiment?

$125$

$250$

$400$

$1000$