1998 AMC 8 Problem 17

Below is the professionally curated solution for Problem 17 of the 1998 AMC 8, 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.

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Concepts:geometric sequence estimation

Difficulty rating: 1120

17.

In how many years, approximately, from $1998$ will the population of Nisos be as much as Queen Irene has proclaimed that the islands can support?

$50$ years

$75$ years

$100$ years

$125$ years

$150$ years

Solution:

The maximal population is $\dfrac{24900}{1.5}=16600.$ This is $83$ times as much as the population in $1998,$ so it would be about $4$ triples from $1998.$ That would be $25\cdot 4=100$ years.

Thus, the correct answer is C .

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