The difference table in each case will give you the answer you need.
For a) the differences repeat, indicating that the function is some kind of exponential.
For b) and c) the 2nd difference is constant which means the function will be a quadratic.
The Gregory-Newton Interpolation formula will give you all 3 answers directly.
A further clue:
for part a) the Gregory-Newton formula is the sum of the binomial coefficients except for the first term.
If you do not know about the Gregory-Newton formula, I suggest you either look it up or find the Mathologer video about it on u-tube.