How to determine number of data points and period of data to determine confidence?

Dear Statisticians

I have done some experiments, with continuously data acquisition, on shrinkage measurements over time. My data shows exponential regression curves. Based on the data I want to estimate how many data points and at what time the data should be gathered, to obtain a certainty of the prediction of the curve. I will use this for future investigations on the same type of shrinkage behavior, but I am trying to reduce the period of data acquisition. Does anyone know how I can do this? or any literature I should look into?

I hope that you can help me!