The correct answer is option A, It will decrease in number
Reason -
Since the red-cockaded woodpecker, depends for its fooding on insects which are found in the trees. As the trees are removed, the insects get simultaneously removed. Now the woodpecker will not get food for feeding itself so the first and foremost affects that will take place is the depletion of woodpeckers due to non-availability of foods. However, after certain period of time the woodpecker population may shift to a new location with appropriate food for survival.