Assume I fill up a 1-liter bottle of water to the brim.
The next day, I empty $\frac 34$th of the bottle, and fill with fresh water until the bottle is full. I shake the bottle thoroughly to mix the water.
The next day, I again empty $\frac 34$th of the bottle and refill with fresh water. Mix again.
My question is: what percent of 1 liter is made up of the original water on the first day after exactly $n$ days?
I believed that the percentage is $\left(\frac 14\right)^n \cdot 100.$
Am I missing something? Or is this correct?