how do you determine if a table is linear, exponential, or quadratic

Answer 1

To determine if a table represents a linear, exponential, or quadratic relationship, you can look at the differences or ratios between consecutive terms in the table.

1. Linear: If the differences between consecutive terms are constant, the table represents a linear relationship. In other words, if you subtract one term from the next and the result is always the same, the relationship is linear.

2. Exponential: If the ratios between consecutive terms are constant, the table represents an exponential relationship. In other words, if you divide one term by the previous term and the result is always the same, the relationship is exponential.

3. Quadratic: If the second differences between consecutive terms are constant, the table represents a quadratic relationship. In other words, if you subtract each pair of consecutive differences and the result is always the same, the relationship is quadratic.

It may also be helpful to plot the data points on a graph and see if they form a straight line (linear), a curve that increases or decreases rapidly (exponential), or a curve that is U-shaped or upside-down U-shaped (quadratic).