I was given the task of writing a formula for the following scenario:
A tank with a capacity of 3,000 cubic meters is filled with a substance. We want that substance, we'll call it substance1, to be diluted by substance2 until substance1 equals 1% of its original volume. Substance2 will be introduced to the tank by filling up a balloon, and then popping it, allowing the substances to mix. Before the balloon and substance2 are introduced to the tank, we need to empty an equal amount from what's already in the tank.
The dilution will occur in steps:
A balloon will be filled with X-Cubic-Meters of substance2.
X-Cubic-Meters will be released from the tank.
The balloon will be put into the tank and popped, allowing the substances to mix thoroughly.
Steps 1 - 3 will repeat until substance1 reaches 1% of its original amount. I believe the problem relates to exponential decay due to how substance1 is both released from the tank, and diluted in each iteration of the process.