The formula which expresses the relationship between $x$ and $y$ as shown in the accompanying table is:
\[\begin{tabular}[t]{|c|c|c|c|c|c|}\hline x&0&1&2&3&4\\\hline y&100&90&70&40&0\\\hline\end{tabular}\]
$\textbf{(A)}\ y=100-10x\qquad\textbf{(B)}\ y=100-5x^{2}\qquad\textbf{(C)}\ y=100-5x-5x^{2}\qquad\\ \textbf{(D)}\ y=20-x-x^{2}\qquad\textbf{(E)}\ \text{None of these}$
Plug in the points $(0,100)$ and $(4,0)$ into each equation. The only one that works for both points is $\mathrm{(C)}.$ Plug in the rest of the points to confirm the answer is indeed $\boxed{\mathrm{(C)}\ y=100-5x-5x^2}$.