For each table of values, find the rule of sequential terms, and determine if the table of values can be described by a linear or exponential equation.

In the first problem, we can try dividing consecutive terms: 14 / 4 = 7 / 2. 49 / 14 is also 7 / 2, and 171.5 / 49 is also 7 / 2. This means that the rule is to multiply by 7 / 2. Because the next term is determined by multiplying by a constant, this is an exponential equation.

In the second problem, we can again divide consecutive terms: 32 / 128 = 1 / 4, 8 / 32 = 1 / 4, and 2 / 8 = 1 / 4. So similar to the first problem, the rule here is to multiply by 1 / 4. And because the next term is determined by multiplying, this is also an exponential equation.

For the third case, taking the quotient between consecutive terms does not reveal any pattern. However, taking the difference does. (-4) - (-9) = 5, 1 - (-4) = 5, and 6 - 1 = 5. This means that the rule is to add 5 for each sequential term. Since the next term is determined by adding a fixed constant, this is a linear equation.