1998 AMC 8 Problem 17

Attempt Problem 17 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).

17.

In how many years, approximately, from 19981998 will the population of Nisos be as much as Queen Irene has proclaimed that the islands can support?
5050 years
7575 years
100100 years
125125 years
150150 years
Answer: C
Concepts:geometric sequenceestimation
Small hint:
Compute how many people the islands can support.
Big hint:
Compare the capacity with the population after each tripling.
Solution:
The maximal population is 24,9001.5=16,600.\dfrac{24{,}900}{1.5}=16{,}600. This is 8383 times as much as the population in 1998,1998, so it would be about 44 triples from 1998.1998. That would be 25⋅4=10025\cdot 4=100 years.
Thus, the correct answer is C .
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