Question

The data in the table represent the height of an object over time.

A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 1, 2, 3, 4. The second column is labeled height (feet) with entries 5, 50, 70, 48, 4.
Which model best represents the data?

quadratic, because the height of the object increases or decreases with a multiplicative rate of change
quadratic, because the height increases and then decreases
exponential, because the height of the object increases or decreases with a multiplicative rate of change
exponential, because the height increases and then decreases

Answer 1

quadratic, because the height increases and then decreases

Reason: the data rise to a peak (at t=2) and then fall. Exponential models are monotonic (constant multiplicative rate) and cannot first increase then decrease, while a quadratic (parabola) naturally rises then falls.