I would like to figure out, or well, to remember how to find the corresponding exponential function between two points based on number of items bought up front i.e. how much discount to give based on the number of items. So for example; One item costs a dollar, but 144 of them costs 84 dollars, which is a full box. Now if I had some people wanting to chip in on purchase of a box, as it could be risky, I would like to offer someone who buys 30 items a greater discount than one who buys 10 of these items. So it is not linear.
I believe it is something of the form $y_1 = C(1 - e^{kt})$ but don't remember how to calculate the constants C and k - but furthermore, I am wondering how I would "tune" it in that I could make discounts greater or less based on the number bought, but still hit the same points of (1,1) and (84,144).
Any thoughts?
Thanks,
Brian