Determine whether the function given by the table is linear, exponential, or neither. If the function is linear, find a linear function that models the data; if it is exponential, find an exponential function that models the data.
\begin{tabular}{|rr|}
\hline$x$ & $f(x)$ \\
\hline-1 & $\frac{8}{7}$ \\
0 & 8 \\
1 & 56 \\
2 & 392 \\
3 & 2744 \\
\hline
\end{tabular}

Step 1 ：The function is not linear because the difference between the y-values is not constant. It could be exponential because the ratio of consecutive y-values seems to be constant. To confirm this, we calculate the ratio of consecutive y-values and check if it is constant. If it is, then the function is exponential and the base of the exponential function is the common ratio.

Step 2 ：We have x = [-1 0 1 2 3] and y = [1.14285714e+00 8.00000000e+00 5.60000000e+01 3.92000000e+02 2.74400000e+03]. The ratios are [7. 7. 7. 7.]. The ratios are all 7, which confirms that the function is exponential. The base of the exponential function is 7.

Step 3 ：Now, we need to find the coefficient of the exponential function. To do this, we substitute one of the points into the exponential function and solve for the coefficient.

Step 4 ：We have x = [-1 0 1 2 3] and y = [1.14285714e+00 8.00000000e+00 5.60000000e+01 3.92000000e+02 2.74400000e+03]. The ratios are [7. 7. 7. 7.]. The solution for the coefficient a is 8.

Step 5 ：Therefore, the exponential function that models the data is \(f(x) = 8 * 7^x\).

Step 6 ：Final Answer: The function is exponential and the exponential function that models the data is \(\boxed{f(x) = 8 \cdot 7^x}\).