If the rabbit population doubles every month and the population at the end of the first month is 32, we can determine the initial number of rabbits by working backward.
At the end of the first month, the population is 32. Since the population doubles each month, the population at the beginning of the first month (initial population) can be found by dividing the end of the first month population by 2:
\[ \text{Initial population} = \frac{\text{Population at the end of the first month}}{2} = \frac{32}{2} = 16 \]
Thus, the initial number of rabbits was 16.