Modeling a Geometric Sequence with a Function

The NCAA women's basketball tournament begins with 64 teams. In each round, one half of the teams are left to compete, until only one team remains.

Below is a table that shows the number of teams for each round. Below the table is a slider with which you can change the starting number of teams. Finally, a scatterplot plots the number of teams versus the round.

Try This

• Change the starting number of teams. You can do this either by dragging the slider thumb or by typing a new number. (You may need to rescale the vertical axis by dragging the top number down.)
• Type an expression in the box at the top of the graph. For example, type 100/x.

Questions

1. How many rounds will a tournament last with 90 teams? How about with 60 teams?
2. How many teams would there need to be for the tournament to last 8 rounds? How about to last 10 rounds?
3. Plot a function on the scatterplot that goes through all the points. Can you make the function so that it will work no matter how many starting teams there are?