Linear Regression coeffiecients used in Exponential Regression

I have a decay curve (y) with values 1, 0.75,0.64,0.54,0.46. The x values are 1,2,3,4,5. First a simple linear regression was performed (y =mx + b). Now the slope and coefficient of this line are used in the following exponential equation to predict the y values for x = (6,7,8).
Exponential equation: y(n) = e^(mx +b) if e^(mx +b) < y(n-1) else y(n) = y(n-1)
m and b are the slope and coefficient of the linear regression
Unfortunately I have only this little part with no explanation.
If anybody could let me know the statistical relevance of such a transformation it would be very helpful. Except the numbers and a lengthy analysis (not statistically relevant in anyway) that follows, I don't have anything to share. Please consider any number of statistically relevant vague assumptions if necessary.
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