Find the exponential function that is the best fit for $f(x)$ defined by the table below.
\begin{tabular}{|c|c|c|c|c|c|}
\hline $\mathbf{x}$ & 1 & 2 & 3 & 4 & 5 \\
\hline $\mathbf{y}$ & 1 & 6 & 11 & 37 & 115 \\
\hline
\end{tabular}
\[
y=\square
\]
(Use integers or decimals for any numbers in the expression. Type an integer or decimal rounded to the near

Step 1 ：The question is asking for an exponential function that best fits the given data. An exponential function has the form \(y = ab^x\).

Step 2 ：We can use the method of least squares to find the best fit. However, this method requires that we take the logarithm of both sides of the equation, which transforms it into a linear equation.

Step 3 ：We can then use linear regression to find the best fit line, and transform it back into an exponential function.

Step 4 ：Given the data points for \(x\) are [1, 2, 3, 4, 5] and for \(y\) are [1, 6, 11, 37, 115].

Step 5 ：Using these data points, we can perform a curve fitting to find the parameters \(a\) and \(b\).

Step 6 ：The best fit exponential function is \(y = a \cdot e^{b \cdot x}\), where \(a\) and \(b\) are the parameters obtained from the curve fitting.