13 The population of Melchester is 185207. During a nationwide flu epidemic the number of new cases in Melchester are recorded each day. The results from the first three days are shown in Fig. 13.
\begin{table}[h]
| Day | 1 | 2 | 3 |
| Number of new cases | 8 | 24 | 72 |
\captionsetup{labelformat=empty}
\caption{Fig. 13}
\end{table}
A doctor notices that the numbers of new cases on successive days are in geometric progression.
- Find the common ratio for this geometric progression.
The doctor uses this geometric progression to model the number of new cases of flu in Melchester.
- According to the model, how many new cases will there be on day 5?
- Find a formula for the total number of cases from day 1 to day \(n\) inclusive according to this model, simplifying your answer.
- Determine the maximum number of days for which the model could be viable in Melchester.
- State, with a reason, whether it is likely that the model will be viable for the number of days found in part (d).