1996 AMC 8 Problem 13

Attempt Problem 13 of the 1996 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 1996 AMC 8 solutions, or check the answer key.

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

13.

In the fall of 1996,1996, a total of 800800 students participated in an annual school clean-up day. The organizers of the event expect that in each of the years 1997,1997, 1998,1998, and 1999,1999, participation will increase by 50%50\% over the previous year. The number of participants the organizers expect in the fall of 19991999 is
12001200
15001500
20002000
24002400
27002700
Answer: E
Concepts:percentagegeometric sequence
Small hint:
A 50%50\% increase multiplies the number by 1.51.5
Big hint:
Apply the factor 1.51.5 three times, for 1997,1997, 1998,1998, and 19991999
Solution:
Each year multiplies the count by 1.5:1.5: 800→1200→1800→2700.800 \to 1200 \to 1800 \to 2700.
So 800⋅1.53=2700800 \cdot 1.5^3 = 2700 participants are expected in 1999.1999.
Thus, the correct answer is E .
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