I'm reading a paper by Yallop and in it he gives the following table of values: $$\begin{array}{|c|c|c|c|c|c|c|}\hline x &0.3 &0.5 &0.7 &1 &2 &3\\ \hline y &? & 8.4 &7.5 &6.4 &4.7 &4.3 \\\hline\end{array}$$
How do I extrapolate to find the value of $y$ when $x=0.3$?
I tried several different ways and all of them give values of $9.3$ or $ 9.4$. However the extrapolated value given by Yallop is $10.0$.
Plotting the data, it looks that we face an exponential function. So, using the available data points and model $$y=a\,e^{bx}+c$$ a nonlinear regression leads to $$y=8.14843\, e^{-1.25978 x}+4.08646 $$ with $R^2=0.999977$ which is very good.
Comparing to the data points, the corresponding computed values are $8.427$, $7.460$, $6.398$, $4.742$ and $4.273$.
Extrapolating the model at $x=0.3$ gives $y=9.670$.
Edit
Using a fit with a cubis polynomial as it seems to be done in the paper, for $x=0.3$, $y=9.502$.