Dynamically non-linear increment

Question

I have a range of percentage like 10% to 80%. Now, I want to divide this range non-linearly in 6 parts so the 2nd part will be greater than 1st.

So minimum value is 10% and it will scale up to 80% and the increase will be greater each time.

Please help me how I can solve this problem?

Answer 1

Quadratic?

$y=10+k*x^2$

x (points)  linear      quadratic
0           10,00000    10,00000
1           21,66667    11,94444
2           33,33333    17,77778
3           45,00000    27,50000
4           56,66667    41,11111
5           68,33333    58,61111
6           80,00000    80,00000

Do yow know how to find k?