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It's been a really long time since I've done calculus or any other kind of math beyond tip calculation. I was given a spreadsheet that calculates and plots a growth curve over time based on a handful of inputs. It goes out for one year. I'd like to be able to make educated (though not necessarily precise) predictions of values along the curve for any amount of time, but if I can avoid it, I'd rather not just extend the length of the spreadsheet. The series is nonlinear, the first values look like this:

540 545 561 599 672 780 904 1,016 1,098 1,151 1,193 1,238 1,297 1,367 1,444

THat's the first ten days of the year, given a 'seed' value of 500 (which of course is one of the variables).

Like I said, I don't need it to be super accurate, just generally describe the slope over time, I just don't know where to even begin figuring out the equation.

Thanks, Paul

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    No, sorry, headspace and timing error. It's one data point per day.2011-01-03

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You are describing a "regression". Depending on how the data looks plotted on a graph, you should choose a type of regression that looks like it will fit the data (quadratic, cubic, linear, exponential, logarithmic, logistic, etc.). However, I would suggest you go to the stackexchange for statistics, since this doesn't really qualify as mathematics. Thanks! (Please note that I mean no disrespect. I am merely pointing out that statisticians will be able to tell you how to avoid common mistakes, like trying to get "too good a fit". There are infinitely many functions that go through a finite number of points, and there is not a unique function that gives a "best fit" without restricting the class of functions (to some of the classes I mentioned above)).

Point of order (Poo): You do not need to do this by hand. Most spreadsheet software supports these types of computations (excel, for instance)!

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    Well, the sample I have is a year (365 data points) and is pretty clearly exponential along those points. But it's modeling online community population growth, which clearly can't be expected to be exponential for all time, I just dont' have any data outside that year.2011-01-04
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I'm not clear on the boundary between mathematics and statistics in this area. Any good book on numerical methods will have routines for extrapolation. My favorite is chapter 3 of Numerical Recipes. Excel has routines for doing this, but a text like NR will have useful cautionary notes.