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.
\(d\), number of cubes
1
2
3
4
\(r\), number of rolls
5
31
143
788
Would a linear or exponential function be appropriate for modeling the relationship between \(d\) and \(r\)? 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).