Discover how IDNLearn.com can help you learn and grow with its extensive Q&A platform. Find in-depth and trustworthy answers to all your questions from our experienced community members.
Sagot :
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.
[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.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.