A national park records data regarding the total fox population over a 12 month period, where means January 1, means February 1, and so on. Below is the table of values they recorded:
t, month01234567891011
F, foxes1501431251007557505775100125143

(a) Is a function of

(b) Let denote the fox population in month . Find all solution(s) to the equation . If there is more than one solution, give your answer as a comma separated list of numbers.