What type of model should be used to make a prediction from the given data? (0,3), (2,4), (5,5), (10,6) linear cubic square root quadratic

It depends on the underlying process that generates the data.

You can always fit N points exactly with a polynomial of degree N-1. A cubic will fit these points exactly. Often, such a polynomial does not give very good predicitions, though.

The next-best choice is a quadratic, followed by a square root, then a linear model.

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In the graph, the model with the highest r²-value is best at predicting the given points. Here are the r² values for the different models.
  linear: 0.9595
  cubic: 1
  square root: 0.9991
  quadratic: 0.9992

If the underlying process is likely to produce points that continue to increase at a slower rate, I'd probably choose the square root model as the most likely to be reasonably accurate. If the points are likely to eventually start decreasing, I'd choose a quadratic model.

221,500 is the answer