Infinite bulk discount algorithm I want to create an algorithm for modelling bulk discounts that do not use set stages for discount (i.e. 10+ items is 10%, 20+ items is 15% discount, etc) and instead can go on indefinitely.
To contextualise, say a product costs £1.
Purchasing 1 products costs £1.00 (0% reduction)
Purchasing 2 products costs £1.90 (5% reduction)
Purchasing 3 products costs £2.73 (9% reduction. +4%)
Purchasing 4 products costs £3.50 (12.5% reduction. +3.5%)
Purchasing 5 products costs £4.213 (15.75% reduction. +3.25%)
And so on. The additional discount for each product added should slowly fall off like a curve and should be able to adjust the power of this curve by tweaking a variable to alter falloff distance.
I'm sure this algorithm must already exist, but I'm unsure of it's name? Also I'm a programmer, layman's terms would be much appreciated.

You could model the cost per item as exponential decay: 
$$
C(n) = n \times C(1)\times (1-d)^{n-1}
$$
where the left side represents the cost of $n$ items. $d$ is the discount rate. If, for example, $d = 0.05$ then the cost per item decreases by $5\%$ for each extra item you buy. You get all the items at the discounted rate.
You could also decide instead to discount each one of the $n$ items at its rate. Then the first one would cost the full amount. Each succeeding one would cost $d$ (percent)  less.
