## 4 Case Studies
### Case Study 3--Carrot  
It was considered for the study of carrot that \(a_{\rm w}=0.983\), \(0.988\) and \(0.993\), resulting in equilibrium relative humidity scenarios of \(98.3\%\), \(98.8\%\) and \(99.3\%\), respectively. The growth of _Aeromonas hydrophilia_, _Bacillus cereus_, _Salmonella_ and _Shigella flexneri_ were studied for this vegetable. The analysis starts at \(T=2\)\({}^{\circ}\)C, at which the onset of proliferation of _Aeromonas hydrophilia_ is verified. For the reasons already mentioned, the study interval is delimited by _Aeromonas hydrophilia_, at \(T=19\)\({}^{\circ}\)C. The study range includes the pH values inherent to the carrot itself, comprised between \(4.9\leq\) pH \(\leq 6.4\). The sampling of the results obtained in the study of carrot concerning the remaining shelf life is shown in Table 8. As seen in the previous case study, at the lowest temperature under analysis (\(T=2\)\({}^{\circ}\)C), when comparing different water activities at the same pH value, a relevant differential is determined, caused by the different relative humidity scenarios proposed. When \(T=2\)\({}^{\circ}\)C and pH = 5.0, for \(a_{\rm w}\) values = 0.983, 0.988 and 0.993, \(t=1096.2\), 689.0 and 451.8 h of remaining shelf life is estimated, respectively. Thus, alternating between minimum and maximum relative humidity scenarios implies a decrease of \(\Delta t=644.4\) h in the remaining shelf life. However, it is seen that this differential decreases significantly as storage temperatures increase. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(T\) (\({}^{\circ}\)C) & pH & \(a_{\rm w}\) &
\begin{tabular}{c} **Remaining Shelf** \\ **Life (\(t\), in Hours)** \\ \end{tabular} & **Contamination by** \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{5.3} & 0.974 & 1580.4 & _Aeromonas hydrophilia_ \\  & & 0.982 & 728.8 & _Aeromonas hydrophilia_ \\  & & 0.990 & 354.6 & _Aeromonas hydrophilia_ \\ \cline{2-5}  & & 0.974 & 1359.0 & _Aeromonas hydrophilia_ \\  & & 0.982 & 628.8 & _Aeromonas hydrophilia_ \\  & & 0.990 & 307.8 & _Aeromonas hydrophilia_ \\ \hline \multirow{4}{*}{10} & \multirow{4}{*}{5.5} & 0.974 & 179.7 & _Bacillus cereus_ \\  & & 0.982 & 102.4 & _Aeromonas hydrophilia_ \\  & & 0.990 & 50.6 & _Aeromonas hydrophilia_ \\ \cline{2-5}  & & 0.974 & 173.4 & _Bacillus cereus_ \\  & & 0.982 & 90.2 & _Aeromonas hydrophilia_ \\  & & 0.990 & 44.8 & _Aeromonas hydrophilia_ \\ \hline \multirow{4}{*}{18} & \multirow{4}{*}{5.7} & 0.974 & 35.8 & _Salmonella_ \\  & & 0.982 & 23.9 & _Aeromonas hydrophilia_ \\  & & 0.990 & 12.0 & _Aeromonas hydrophilia_ \\ \cline{1-1} \cline{2-5}  & & 0.974 & 34.9 & _Salmonella_ \\ \cline{1-1}  & & 0.982 & 21.7 & _Aeromonas hydrophilia_ \\ \cline{1-1}  & & 0.990 & 11.0 & _Aeromonas hydrophilia_ \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sampling of results of DSS—Remaining shelf life of onion. When comparing different pH values under the same conditions of temperature and water activity, there is a rather considerable difference at low temperatures, which gradually becomes residual at higher temperatures. At \(T=2\)\({}^{\circ}\)C and \(a_{\rm w}=0.988\), shelf life assumes \(t=829\) h when pH = 4.9 and \(t=689\) h when pH = 5.0, a difference of \(\Delta t=140\) h. When storage temperature assumes a value of \(T=10\)\({}^{\circ}\)C and the water activity value remains unchanged (\(a_{\rm w}=0.988\)), shelf life is \(t=126.4\) h for a pH = 4.9 and \(t=123\) h for a pH = 5.0, that is, a difference of \(\Delta t=3.4\) h. At the most unfavourable scenario for bacterial growth, minimum water activity, temperature, and pH values (\(a_{\rm w}=0.983\); \(T=2\)\({}^{\circ}\)C; pH = 4.9), the shelf life \(t=1321.6\) h after the horticultural batch enters storage is established at the threshold of contamination by _Aeromonas hydrophila_ (the only bacterium capable of replicating under the selected conditions).