To model the data using a logarithmic function, we can use the form:
[tex]\[ y = a \ln(x) + b \][/tex]
where \( \ln(x) \) represents the natural logarithm of \( x \), and \( a \) and \( b \) are constants that we need to determine.
Given the data points:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 60 \\
\hline
2 & 54 \\
\hline
3 & 51 \\
\hline
4 & 50 \\
\hline
5 & 46 \\
\hline
6 & 45 \\
\hline
7 & 44 \\
\hline
\end{array}
\][/tex]
we need to find the best values for constants \( a \) and \( b \) that fit this logarithmic model to the given data points. After performing the necessary calculations and fitting the logarithmic model to the data, we determine the values of \( a \) and \( b \).
The fitted parameters are:
[tex]\[ a = -8.245225947626354 \][/tex]
[tex]\[ b = 60.04169738027974 \][/tex]
Therefore, the logarithmic function that models the provided data is:
[tex]\[ y = -8.245225947626354 \ln(x) + 60.04169738027974 \][/tex]
This function captures the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] based on the given data points.
