# Bending algorithm needed

Can someone help me with the formula needed to obtain the following. I need to discount products on a sliding scale. If a customer purchases 2 products, he must get a 15% discount. If he purchases 10, he must get a 30% discount. I don't want a linear slope, but rather as the number of products increases, the increase in the discount decreases.

2 => 15%
4 => ≈20%
10 => 30%


I need to formula with this, which should include a bend factor.

I know how do to this for FV, IV, but not this.

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You might want your discount function something like $$d(n) = 100 k_1 \times (1 - e^{-k_2 n})$$ where $d(n)$ is the percentage discount and $n$ is the number of products purchased and $k_1, k_2$ are constants with $0 < k_1 \leq 1$.
EDIT: Choose $k_1 = 0.31$ and $k_2 = 0.35$.