# 1996 AJHSME Problems/Problem 13

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## Problem

In the fall of 1996, a total of 800 students participated in an annual school clean-up day. The organizers of the event expect that in each of the years 1997, 1998, and 1999, participation will increase by 50% over the previous year. The number of participants the organizers will expect in the fall of 1999 is $\text{(A)}\ 1200 \qquad \text{(B)}\ 1500 \qquad \text{(C)}\ 2000 \qquad \text{(D)}\ 2400 \qquad \text{(E)}\ 2700$

## Solution 1

If the participation increases by $50\%$, then it is the same as saying participation is multipled by a factor of $100\% + 50\% = 1 + 0.5 = 1.5$.

In 1997, participation will be $800 \cdot 1.5 = 1200$.

In 1998, participation will be $1200 \cdot 1.5 = 1800$

In 1999, participation will be $1800 \cdot 1.5 = 2700$, giving an answer of $\boxed{E}$.

## Solution 2

Since the percentage increase is the same each year, this is an example of exponential growth with a base of $1.5$. In three years, there will be $1.5^3 = \frac{27}{8}$ times as many participants. Multiplying this by the $800$ current participants, there are $2700$ participants, and the answer is $\boxed{E}$.

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