Game 1 gives you 200 points every time you score. Game 2 doubles your points every time you score (2, 4, 8, and so on). In which game do you think you will you earn more points?Explain your answer.

It depends on how many times you score. In Game 1, each score adds 200 points, so after n scores you have 200n points. In Game 2, the points double each time, so after n scores the total is 2 + 4 + 8 + … + 2ⁿ. With only a few scores, Game 1 may give more, but with enough scores, Game 2’s rapidly growing points will overtake it; for example, after 8 scores Game 1 gives 1,600 points while Game 2 gives 510. So the best answer is “not sure/it depends.”

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