I'm sure this statistical issue has been solved before, but I had a heck of a time googling it. I hope someone here can recommend a method for dealing with this problem!

I am trying to measure the rate of conversion from cell type A to cell type B. After adding inducer, I take an aliquot every few hours and run it through a flow cytometer to figure out what fraction of cells are still cell type A. The data for a single run looks vaguely like this:

1 hr: 100% type A
2 hr: 50% type A
3 hr: 25% type A

etc. I take the log of each data point and fit a slope (an estimate of the conversion rate). Of course, the slope is usually not a perfect fit like in these sample data, so I record the confidence interval of the fitted slope.

Okay, so here's the problem. I repeat this experiment three times and I get three slopes and their corresponding confidence intervals. I would like to use this data to estimate the true slope and calculate a confidence interval for the measurement. Does anybody know how to do this properly?

Thanks in advance!