1998 AMC 8 Problem 16

Attempt Problem 16 of the 1998 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1998 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

16.

Estimate the year in which the population of Nisos will be approximately 6000.6000.
20502050
20752075
21002100
21252125
21502150
Answer: B
Concepts:geometric sequenceestimation
Small hint:
Compare 60006000 with the starting population 200.200.
Big hint:
Three triplings are close to a factor of 30.30.
Solution:
This would be the year the population is 3030 times as much as in 1998.1998. This means the population triples approximately 33 times, making the year approximately 3⋅25=753\cdot 25=75 years after 1998.1998. This would be 2073,2073, so 20752075 is the best approximation.
Thus, the correct answer is B .
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