3 In the first week of an outbreak of influenza, 9 patients were diagnosed with the virus at a medical practice in Pencaster. Records were kept of \(y\), the total number of patients diagnosed with influenza in week \(n\). The data are shown in Fig. 3.
\begin{table}[h]
| \(n\) | 1 | 2 | 3 | 4 | 5 |
| \(y\) | 9 | 32 | 63 | 96 | 125 |
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{table}
- Complete the difference table in the Printed Answer Booklet.
- Explain why a cubic model is appropriate for the data.
- Use Newton's method to find the interpolating polynomial of degree 3 for these data.
In both week 6 and week 7 there were 145 patients in total diagnosed with influenza at the medical practice.
- Determine whether the model is a good fit for these data.
- Determine the maximum number of weeks for which the model could possibly be valid.