Example: In a woman's professional tennis tournament, the money a player wins depends on her finishing place in the standings. The first-place finisher wins half of $1,500,000 in total prize money. The second-place finisher wins half of what is left ; then the third-place finisher wins half of that, and so on. a) Write a rule to calculate the actual prize money in dollars won by the player finishing in nth place, for any positive integer n. b) Graph the relationship between the first 10 finishers and the prize money in dollars. What pattern is indicated in the graph? What type of relationship exists between the two variables?