A store has two managers, one who believes that high profits come from lowering prices and getting more customers and another who believes that high profits come from raising prices and making more profit per customer. These managers get to choose prices in alternate weeks. For each case, In week 1, the “low price” manager cuts prices by 50%. In week 2, the “high price” manager raises prices by 50%, and so forth. Suppose an item started out at $100.a. Find the price after 1, 2, 3, and 4 weeks.b. Find a formula for the price after t weeks (break into the two cases, t even and t odd).c. Which of the managers wins?

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