I'm building a program that calculates the cost of an item based on it's size (let's say a bamboo pole). As the customer requests a longer pole, it gets hard to find a bamboo, plus requires more resources to grow, therefore, I would want to charge more per inch for the piece of bamboo based on it's length approaching a particular length. Then after that point the cost per inch would really escalate.
I believe that log would be the function that I need to use, but I just can't figure out how to make my formula. I've tried log(-x), log(x-1), log(y-x), I can't figure out how to get the log to shoot up to infinity, nor target a specific point.
Referencing the example above, I would want the cost/inch of the bamboo to stay reasonable up to 72", but after that, the cost/inch should rapidly increase, until it gets to 100", where it would become ridiculously expensive. Before 72", it should rise in cost/inch, but at a slow rate (it costs a little bit more per inch to grow a 72" stick than a 6" stick). I'm looking for a uniform growth, not a split formula. No f(x) where x<72, g(x) where x>72.
I'm not necessarily looking for the formula to solve the above question. I am looking for the HOW to research and solve the above question.
Many Thanks, Matt
You are looking for functions that go to infinity, preferably in finite time (vertical asymptote) or something similar. you then construct a scale to get to your infinity point at the number of inches you want (say 100). so, for tan(x) as an example, pi/2 is infinity, so map 0-100 to pi/4-pi/2, and you have something that works (you might want to add a constant to formula to help you on on the low end).
A possibility: f(x) = Tan(x/200*pi/2+pi/4)+5
f(10) = 6.2
f(72) = 9.5
f(90) = 17.7
f(95) = 35.45
f(98) = 68.7
Feel free to massage the constants, or pick a different function to get the behavior that you want.