For the data $(1, 2),\ (2, 5),\ (3, 10),\ (4, 17)$, the first differences are $3, 5, 7$. What are the second differences, and what function family does this suggest?

Second differences are $2$; Quadratic

Second differences are $2$; Linear

Second differences are $3$; Exponential

Second differences are $2$; Exponential

A dataset has first differences of $2, 4, 8, 16$. Which method should you apply next to correctly identify the function family?

Check if the second differences are constant

Check if the successive ratios are constant

Check if the first differences are constant