## 3 Results and Discussion
### Application of (HS-SPME) Method for Evaluating the Persistence of Safrole in Cowpea Beans  
Different mathematical models were tested to explain the safrole-residue degradation in cowpea beans treated with PHEO, both by contact and fumigation (Table 4). For contact-treated grains, the best fit was the exponential model (y = ae\({}^{\text{bx}}\) + c) (Figure 5a), with \(R^{2}\) = 0.96, RMSE = 0.077, and \(P\) = 0.043. On the other hand, the best fit for fumigated grains was the logarithmic model (y = y\({}_{0}\) - a ln (\(x-x_{0}\))) (Figure 5b), with \(R^{2}\) = 0.97, RMSE = 0.14, and \(P\) = 0.034. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Treatment** & **Model** & **Equation** & \(\mathbf{R^{2}}\) & **RMSE b** & \(\mathbf{P}\) \\ \hline \multirow{4}{*}{Contact} & Linear & \(y=-\) 0.0079 \(x\) + 0.67 & 0.46 & 0.27 & 0.21 \\  & Quadratic & \(y=0.0002x^{2}\) \(-\) 0.025\(x\) + 0.86 & 0.58 & 0.25 & 0.42 \\  & Exponential & \(y=10.54\text{exp}^{-0.4861x}\) + 0.17 & 0.98 & 0.08 & 0.043 \\  & Potential & \(y=18.06(1+x)\)\({}^{-1.5842}\) & 0.88 & 0.13 & 0.018 \\  & Logarithmic & \(y=-0.065\text{ln}\)\((x\) \(-\) 5.0000) + 0.40 & 0.98 & 0.49 & 0.021 \\ \hline \multirow{4}{*}{Fumigation} & Linear & \(y=-\) 0.018\(x\) + 1.5 & 0.64 & 0.43 & 0.10 \\  & Quadratic & \(y=0.0004x^{2}\) \(-\) 0.052\(x\) + 1.9 & 0.76 & 0.38 & 0.24 \\ \cline{1-1}  & Exponential & \(y=6.53\text{exp}^{-0.2606x}\) + 0.38 & 0.89 & 0.24 & 0.11 \\ \cline{1-1}  & Potential & \(y=11.16(1+x)\)\({}^{-0.95}\) & 0.92 & 0.21 & 0.011 \\ \cline{1-1}  & Logarithmic & \(y=-\) 0.27\(\text{ln}\)\((x\) \(-\) 4.94) + 1.4 & 0.97 & 0.13 & 0.034 \\ \hline \hline \end{tabular}  
* Coefficient of determination and b  
\end{table} 
Table 4: Mathematical-model fitting for safrole residues in cowpea beans treated with _Piper hispidin-ercum_ essential oil, either by contact (a) or fumigation (b), throughout storage. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Theoretical Concentration** & **Nominal Concentration \(\pm\)1 SE** & **Accuracy (n = 6)** & **Precision** \\ \hline
**(ug kg\({}^{-1}\))** & **(ug kg\({}^{-1}\))** & **Recovery (\%)** & **2 CV (\%)** \\ \hline
0.019 & 0.018 \(\pm\) 0.0010 & 99.26 & 12.76 \\
0.095 & 0.094 \(\pm\) 0.0057 & 100.48 & 14.82 \\
0.190 & 0.196 \(\pm\) 0.012 & 104.85 & 14.61 \\ \hline \hline \end{tabular}  
* SE = standard error; 2 CV = coefficient of variation.  
\end{table} 
Table 3: Accuracy and precision of the headspace solid-phase microextraction method coupled with a gas chromatograph with flame ionization detector for extraction of safrole from cowpea beans. Safrole residue was evaluated throughout storage. The concentrations detected in the contact-treated grains were 1.095 kg\({}^{-1}\) and 0.052 ug kg\({}^{-1}\), after 5 and 90 days, respectively. For fumigated grains, the safrole residue levels were 2.16 ug kg\({}^{-1}\) and 0.12 ug kg\({}^{-1}\), after 5 and 90 days. Overall, by the fifth day of storage, the safrole levels in the grains was reduced by 99%. The safrole concentrations found in the cowpea-bean after treatments are lower than the limits set for beverages and foodstuff by Codex Alimentarius and Anvisa [40; 41]. Nonetheless, these dose levels proved to control pests in stored cowpea beans, such as C. _maculatus_. The effect of residual PHEO on C. _maculatus_ and _Stiophilus zeamais_ Mots. (Coleoptera: Curculionidae) was investigated in cowpea beans and corn grains stored for up to 120 days by [PERSON] et al. [55] and [PERSON] et al. [25], respectively. The toxicity of PHEO was the highest right after grain contamination, with values ranging from 100 to 93.8% mortality. After 30 days of storage, a low residual effect was noticed, with less than 17.5% mortality. In the present study, 99% of PHEO degradation occurred after 5 days of storage, which may explain the low toxicity found by [PERSON] et al. [55] and [PERSON] et al. [25] after 30 days of storage. Studies showed that botanical insecticides have low persistence in stored products [25; 55; 56].