Growing E.coli to a specific pH. I'd like to have an idea of what a graph of pH vs time looks like.?

I'd like to know how long it is going to take to get from a starting point near pH5.3 to a pH of 7.5. If you have a reference for this or just a good idea of how long it might take, it would be lovely. For bonus points: I'm using a phosphate buffered growth media and C41 bacteria.