How to find optimal data range to fit exponential trendline?

It is difficult to be specific with only the chart presented, because I would not use the chart at all to do this (except maybe as a visualization of the final solution found). Here's what I would probably try first (note that I am assuming the data are arranged in columns, not rows. Adjust as needed):

0) Recall that exponential regression is really just simple linear regression on the transformation of the data LN(y)=mx+b, so add a column to compute LN(y_value).
1) Enter row and height parameters for an OFFSET() function (https://support.office.com/en-us/art...e-b4d906d11b66 ). The OFFSET() function will be used to select the range to test from the data set.
2) Nest the OFFSET() function inside of an RSQ() function (https://support.office.com/en-us/art...d-a8364f2be08f ). This will compute the R2 value for the chosen subset of data. =RSQ(OFFSET(first_known_y_cell,row_offset_cell,0,height_cell,1).
3a) Try Solver to see if Solver can find the optimum. This is the kind of problem that Solver doesn't always do well with, but, if it works, it should be fairly easy. Set up Solver to (A) Set Target Cell -- RSQ() cell (B) to a maximum (C) by changing: the row offset and height cells (D) subject to the constraints that row offset and height are integers greater than 0 and height cell is larger than whatever minimum you think it should use and (E) using an Evolutionary algorithm. Let Solver try to solve this.
3b) If Solver fails or takes a very long time (because it probably really just has to try every possible subset of the data and it doesn't always do well with problems requiring a brute force "just try every possible combination and see which is best" approach), build your own "combinatorial algorithm" in the spreadsheet that will compute the different combinations of row offset and height and subsequent RSQ() values, then locate the MAX() of all of the computed RSQ(). I put together this example that shows a couple of ways to generate permutations that should help show how this might be accomplished: https://www.excelforum.com/tips-and-...thout-vba.html
4) Once you know which subset generates the MAX() RSQ(), then you can use the LOGEST()or LINEST() function to compute the regression parameters for that subset.

That's a quick overview, what part(s) do you need further help with?