What word best fits this definition."this is to estimate a value by following a pattern and going beyond the values already known"

Extrapolation

Extrapolation only works if the data is truly fitting of some function or pattern. Often, we won't know what the function for a scatterplot will be so making extrapolations could lead to errors.

Example of extrapolation working: You drive for 1 hour and travel 60 miles, 2 hours gets you 120 miles, 3 hrs you go 180 miles. You can successfully extrapolate that you'll go 240 miles if you drive for 4 hours (assuming you keep the speed up). The formula that fits the data is y = 60*x with x as the time in hours and y as the distance traveled.

Example of extrapolation falling apart: It rained yesterday and it rains today; therefore it will rain tomorrow. The flaw here is that it might clear up tomorrow and not rain at all. Unfortunately weather isn't that simple. There are a lot of factors at play.

the monthly balance will be $75,000