Hello. I know people have posted similar questions about using an existing
relationship between X and Y to predict new Ys given new Xs but I think mine
has a slightly different twist. I would appreciate any help that could be
offered.

I have 20 data points for both X and Y. Each X point represents the number
of workers on a farm for a particular year over a 20-year period. Each Y
point represents the amount of crop harvest each year over that same period.
The data is from 1901 to 1920. When I plot the points and fit an exponential
trend line I get a high R-square of .9 . I would like to assume that the
number of workers for that same 20-year period was actually 20% lower than
the actual number of workers. Using this new population of workers I would
like to predict the new amount of crop that could be harvested. When I do
this using the function: Growth(known_y's,known_x's,new_x's,const) I get
results that do not seem to be intuitively correct. For example, the new
population in 1916 is approximately equal to the actual population in 1908
but the amount of crop that is expected to be harvested differs widely.

Thanks in advance for any help. I would be happy to send the actual numbers
I'm working with if that would be helpful in clarifying my question.