How would I find the instantaneous rate of change using this formula y=3.9657(0.9982^x) and given a table of values?

y = ab^x

ln y = lna + x lnb
1/y y' = ln b
y' = y ln b
The instantaneous rate of change is just (ln b) times the current value.

That is the very definition of exponential change. The rate of change is proportional to the current value.