Mai used a computer simulation to roll number cubes and count how many rolls it took before all of the cubes came up sixes. Here is a table showing her results.
, number of cubes
1
2
3
4
, number of rolls
5
31
143
788
Would a linear or exponential function be appropriate for modeling the relationship between and ? Explain how you know.
Which of these functions decays the most quickly? Which one decays the least quickly?
Graph of three decreasing exponential functions, xy-plane, origin O. Horizontal axis, scale 0 to 6, by 1’s Vertical axis, scale 0 to 12, by 2’s. Function X is red and has these points: (0 comma 10), (3 comma 3), and (4 comma 2). Function Y is blue and has these points: (0 comma 10), (1 comma 6) and near (4 point 5 comma 1). Function Z is green and has these points: (0 comma 10), near (1 comma 2 point 5) and near (2 comma point 6).