Every 4 years, the population of the town of Arloe doubles. On December 31, 2008, the population of Arloe was 3456. What was the population on December 31, 1988?
(A) 54
(B) 576
(C) 216
(D) 108
(E) 864
Solution 1

From December 31, 1988 to December 31, 2008, a total of 20 years have elapsed.

A time period of 20 years is the same as five 4 year periods.

Thus, the population of Arloe has doubled 5 times over this period to its total of 3456 .

Doubling 5 times is equivalent to multiplying by $2^{5}=32$.

Therefore, the population of Arloe on December 31, 1988 was $\frac{3456}{32}=108$.

## Solution 2

The population doubles every 4 years going forward, so is halved every 4 years going backwards in time.

The population on December 31, 2008 was 3456 .

The population on December 31, 2004 was $3456 \div 2=1728$.

The population on December 31, 2000 was $1728 \div 2=864$.

The population on December 31, 1996 was $864 \div 2=432$.

The population on December 31, 1992 was $432 \div 2=216$.

The population on December 31, 1988 was $216 \div 2=108$.

ANSwER: (D)