AMC 8 1991 Problem 25

An equilateral triangle is originally painted black. Each time the triangle is changed, the middle fourth of each black triangle turns white. After five changes, what fractional part of the original area of the black triangle remains black?

$\text{(A)}\ \frac{1}{1024} \text{(B)}\ \frac{15}{64} \text{(C)}\ \frac{243}{1024} \text{(D)}\ \frac{1}{4} \text{(E)}\ \frac{81}{256}$