You are not logged in.
I'm trying to derive a learning curve formula, using the x-axis for elapsed time and the y-axis for the percent of acquired knowledge/skill. Assuming the curve begins at 0,0 and the estimate of learning reaches 95% after n units of time, what would the formula be for this linear function? (The asymptote would have a y value of 1.) I'd really appreciate your help because I've forgotten if this is even enough information to write the formula. I want to assume that the learner never actually reaches 100% but keeps getting closer to it over time.
Offline
How do you know it is a hyperbola and not an exponential decay toward 100%?
Last edited by John E. Franklin (2006-10-05 12:15:56)
igloo myrtilles fourmis
Offline
Ah, well, I don't - know that it's a hyperbola. What I'm really after is an approximation (key word) of productivity, given that learning "appears" to be complete after a certain duration. And I'll assume that, say, 95% learning equates to "trained" and that more learning happens over time, but resulting in a negligible increase in productivity. I've looked at write-ups for learning curves but they all seem to be based on tracking the number of units completed (say, per day) and this problem is more subjective, a qualitative measurement rather than a quantitative one.
Make sense? It's just something that got stuck in my craw and I can't seem to let go of it. I'd really appreciate it if you can put me in the ballpark.
Offline
As John said, an exponential approaching 100% might work nicely.
It has an asymptote at y = 1.
Such a curve would be:
Where k would be a rate constant.
Offline
OK - thanks. I feel like I'm getting somewhere, except I'm not familiar or have forgotten the notation. I don't know what e & t represent, and I don't know what you mean by "rate constant." Sorry.
Offline
t is the independent variable, which would be time in this case, on the horizontal axis.
e is the base of the natural logarithm, and is equal to about 2.718281828
e^t is just the standard exponential function that is used to model all kinds of exponential growth in science.
here is an example of such a curve (the top one in this picture):
http://cognitrn.psych.indiana.edu/busey/WWWPubs/PsychRev/Image2.gif
k, which I called a rate constant, is a number that determines how sharply the curve rises at the beginning.
If k = 100 for example, it will rise very sharply, if k = 1, the rise is moderate.
I would suggest plotting a few of these with graph plotting software, like Winplot (which is free and easy to use).
Last edited by polylog (2006-10-09 11:25:03)
Offline
Ah - PERFECT! That's EXACTLY what I was after and it works GREAT! Thank you very much!
Offline
Cool.
Offline