I don't think there's a one-word name for such a situation.
Depending on exactly what you want to do with the data when you are done, you might be looking for Segmented (Piecewise) Regression. It is clear that after a "breakpoint" in your model1, you experience completely linear behavior ($x > 3$). The first part looks quadratic.
Let's split our database into two separate lists:
Quadratic 1 10 2 60 3 72 Linear 4 70 5 69,8 6 69,6 7 69,4 8 69,2 9 69 10 68,8 11 68,6 12 68,4 13 68,2 14 68 15 67,8 16 67,6
Run regression on the first data set, receiving $f_1(x) = -19x^2 + 107x - 78$.
Run regression on the second data set, receiving $f_2(x) = -0.2x + 70.8$.
Now create the piecewise function: $ f(x) = \left\{ \begin{array}{lr} -19x^2 + 107x - 78 & (x \le 3)\\ -0.2x + 70.8 & (x > 3)\\ \end{array} \right. $
Perhaps we want such a function to be continuous. If you want, you can set the two function equal to each other, and you will find they intersect2 at $3 \le \dfrac{268+2\sqrt{286}}{95} \approx 3.17708 \le 4 $. So you could write: $ f(x) = \left\{ \begin{array}{lr} -19x^2 + 107x - 78 & (x \le 3.17708)\\ -0.2x + 70.8 & (x > 3.17708)\\ \end{array} \right. $
Now your function is continuous as well.
I would definitely recommend the piecewise regression method, but by using symbolic regression and the software Eureqa, I was able to find a quite interesting formula:
$ 70.8 \cdot \mathrm{logistic}(3.541x - 5.323) - 0.2x $
Where $\mathrm{logistic}(x) = \dfrac{1}{1 + e^{-x}}$, which is a quite common function, so you should have no trouble describing it.
If I was describing it to a friend, I would probably say "a logistic function followed by a linear decrease" or perhaps "a logistic function".
Some stats:
- $ R^2 \approx 0.999 $
- Maximum error at $x=3$ with $\approx 2.151$
- $\mathrm{MSE} \approx 0.309 $
1 There are varying algorithms for determining breakpoints, one such algorithm is listed briefly here.
2 Is this allowed? Will this always be the case? Perhaps an algorithmic approach would be better.