Question

which situation is most likely to have a constant rate of change?

a. the number of people inside a basketball arena compared with the amount of time since the arena opened

b. the number of teeth a child has compared with her age

c. the number of bottles of orange juice in a grocery store compared with the day of the month

d. the distance of a run compared with the number of times around a track

Explanation:

• Option A: People enter/leave a basketball arena unevenly (e.g., rush at start, lulls), so rate of change isn’t constant.
• Option B: A child’s teeth growth isn’t constant (teeth come in at different rates/ages, like baby teeth then adult teeth), so rate varies.
• Option C: Grocery store orange juice stock changes due to random restocking, sales, etc., not at a constant rate per day.
• Option D: Each time around a track is a fixed distance (e.g., a track is 400m, so each lap adds 400m). So distance = laps × track length, which is a linear relationship with a constant rate (track length per lap).

Answer:

D. The distance of a run compared with the number of times around a track