A question concerning the strength of synapses
What you are describing is exactly how long-term potentiation/LTP (or depression/LTD, for that matter) is measured electrophysiologically.

Here's an example from a 1988 review by Nicoll et al:



Nicoll, R. A., Kauer, J. A., &amp; Malenka, R. C. (1988). The current excitement in long term potentiation. Neuron, 1(2), 97-103.

The x-axis is time in minutes, the y-axis is a measure of synaptic strength: the slope of the local field potential response to simulation of a particular pathway. You could also measure an EPSP internally, measure voltage with a voltage-sensitive dye, etc.

At the point marked "tetanus", a long train of pulses is delivered that is known to cause LTP. Afterwards, you see an increase in synaptic strength that is maintained for many minutes.

It's also possible to perform these experiments over longer time scales, with different paradigms, in the presence of various drugs that influence LTP, etc. Different protocols will give different durations of LTP.

These sorts of plots are ubiquitous in the LTP/LTD research field, so if you read any papers in that area you are likely to come across many similar presentations.