No calculus here is required. If the tank takes up 2.5ppm, and you can add a maximum of 7.5ppm, then that's 5ppm that you can add per day, which means you need 10 days to get from 360ppm to 410ppm.
I'm a little rusty on my calculus and was wondering if I can get a little help. The problem involves linear dosing a Ca solution into an aquarium to increase the total concentration. Here are the numbers:
initial concentration: 360ppm
uptake: 2.5ppm per day
dosing adds: 7.5ppm per day
target concentration: 410ppm
So in words, the tank starts at 360ppm and I would like to get the concentration to 410ppm. Only one dose is allowed per day which adds 7.5ppm to the total concentration, but the uptake of the system consumes 2.5ppm per day. How many days/doses are needed to get 410ppm?
This is the instantaneous equation I came up with:
[(Target Ca conc - Ca conc + Ca consumed)] /[dosage amt] = #times you have to dose