Solution:
Given the table;
The graph of the points is;
(a) The logarithm model for the data using the first and last data points in the table is;
[tex]\begin{gathered} F=4.26\ln(I)+8.95 \\ \\ \text{ Where }F\text{ is the fusion frequency;} \\ \\ I\text{ is the light intensity} \end{gathered}[/tex]
(b)
[tex]\begin{gathered} F=4.26\ln(48.4)+8.95 \\ \\ F=25.48 \\ \\ F\approx25.5 \end{gathered}[/tex]
Thus, the difference between the model value and the observed value is approximately 1.2. The model predicts a frequency of 25.5 as compared to the observed frequency of 25.3
(c)
[tex]\begin{gathered} 35.2=4.26\ln(I)+8.95 \\ \\ 4.26\ln(I)=35.2-8.95 \\ \\ \ln(I)=\frac{26.25}{4.26} \\ \\ I=474.4 \end{gathered}[/tex]
Thus, the difference between the model intensity and the observed value is approximately 37.1. And that is quite a wide difference. The model predicts an intensity of 474.4 as compared to the observed intensity of 437.3
