AMC 8 1998 Problem 16
AMC8 1998 年第 16 题
数列与规律★★★☆☆
Estimate the year in which the population of Nisos will be approximately 6,000.
在 Irenic 海的中央坐落着美丽的 Nisos 群岛。1998 年这些岛屿上的人口仅为 200，但人口每 25 年翻三倍。Irene 女王已颁布法令，岛上每个人必须有至少 1.5 平方英里的空间。Nisos 群岛的总面积为 24,900 平方英里。
估计 Nisos 人口大约达到 6,000 的年份。
- A.2050
- B.2075
- C.2100
- D.2125
- E.2150
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
We could triple the population every 25 years and make a chart:
Year: 2000 Population: 200
Year: 2025 Population: 600
Year: 2050 Population: 1800
Year: 2075 Population: 5400
Year: 2100 Population: 16200
The closest year is 2075, or
We could find out how many periods of 25 years we need to triple by dividing our total from our present number.
The power of 3 that 30 is closest to is
Therefore, after 3 periods, we will be closest to 6000.
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