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Linear Growth vs. Exponential Growth

Question 1 • 26/27 ALGEBRA II A

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?game 1game 2not sure/it dependsExplain your answer.

Answer
A
game 1
B
game 2
C
not sure/it depends

Explanation

It depends on how many times you score. In Game 1, you earn 200 points per score, so after 3 scores you have 600 points. In Game 2, the points are 2, 4, and 8, totaling 14 after 3 scores. But Game 2’s points double each time, so with enough scores it can eventually earn more. Without knowing how many times you’ll score, you can’t tell which game gives more points.

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