AMC 8 1996 Problem 13
AMC8 1996 年第 13 题
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In the fall of 1996, a total of 800 students participated in an annual school clean-up day. The organizers of the event expect that in each of the years 1997, 1998, and 1999, participation will increase by 50% over the previous year. The number of participants the organizers will expect in the fall of 1999 is
1996 年秋季，共有 800 名学生参加了一年一度的学校清洁日。活动组织者预计在 1997、1998 和 1999 年每年，参与人数将在前一年的基础上增加 50%。组织者预计 1999 年秋季的参与人数是
- A.1200
- B.1500
- C.2000
- D.2400
- E.2700
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
If the participation increases by 50%, then it is the same as saying participation is multipled by a factor of 100% + 50% = 1 + 0.5 = 1.5.
In 1997, participation will be .
In 1998, participation will be
In 1999, participation will be , giving an answer of .
Since the percentage increase is the same each year, this is an example of exponential growth with a base of 1.5. In three years, there will be times as many participants. Multiplying this by the 800 current participants, there are 2700 participants, and the answer is .
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