In my math class we are doing are doing a modeling task where we have to find a quadratic, cubic and other polynomial model for a given data set.

The table below is for a fishing rod with eight guides plus a guide at the tip of the rod.

Code:

guide # | distance
from tip | from tip
---------+---------
1 | 10
2 | 23
3 | 38
4 | 55
5 | 74
6 | 96
7 | 120
8 | 149
---------+---------

and the total length of the fishing rod in 230 cm.

So far all the polynomial models create an upward curve, do you have any ideas for any better functions that could model this data?

Since the distance from the tip cannot be more than 230 cm, would that make the polynomial models wrong because they go higher than 230 cm?