Question

Analyzing a Real-World Scenario
Rachel found the following rate of change for the scenario represented in this table.

A 2-column table with 5 rows. Column 1 is labeled Time (hours) with entries 4, 5, 6, 7, 8. Column 2 is labeled Berries picked with entries 128, 181, 234, 287, 340.

What can you conclude from her work?
Check all that apply.
The scenario is represented by a linear function, since the rate of change is constant.
The scenario is represented by a nonlinear function, since the rate of change is constant.
The berries are picked at a constant rate of 53 per hour.
The berries are not picked at a constant rate.

Answer 1

Compute successive differences: 181−128 = 53, 234−181 = 53, 287−234 = 53, 340−287 = 53. The rate of change is constant (53 berries per hour), so the data is linear.

Therefore: select the first and third statements. The second and fourth are false.

(If you want the linear rule: B(t) = 53t − 84, where t is hours.)