The answer is three significant figures. The 1 and the 7 are both significant, because they are non-zero quantities.
This is where significant figures gets a little more complicated, because if a zero is used as a placeholder (i.e. 0.00027 cm) then it is insignificant.
But in the case above, the zero isn't being used as a placeholder, and thus, is significant.
To write the function correctly, it is important to assign variables correctly and understand the situation of the problem clearly. For this, we let y the number of people and x as the number of songs played.
At x = 0 y = 567
at x = 1 y = 567 - 567(1/3)
at x = 2 y = 567 - 567(1/3)(1/3)
at x = 3 y = 567 - 567(1/3)(1/3)(1/3)
Therefore, the number of people left after x songs would be represented by the equation:
y = 567 - 567(1/3)x
y = 567 ( 1- x/3 )
218,900 should be the answer
