1998 AMC 8 Problem 16

Below is the professionally curated solution for Problem 16 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: 1030

16.

Estimate the year in which the population of Nisos will be approximately $6000.$

$2050$

$2075$

$2100$

$2125$

$2150$

Solution:

This would be the year the population is $30$ times as much as in $1998.$ This means the population triples approximately $3$ times, making the year approximately $3\cdot 25=75$ years after $1998.$ This would be $2073,$ so $2075$ is the best approximation.

Thus, the correct answer is B .

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