**3.2 Statistical models regarding the phenomenon of accumulation of heavy metals in plants studied**

Using the numerical data from the experiments, the statistical mathematical models were obtained by interpolation.

• Interpolation formulas for the amount of heavy metal accumulated at the end of vegetation period

The general form of the interpolation polynomials (degrees one - four) is (Eq. (14)):


$$\mathbf{C}\_{p}(\mathbf{C}\_{\rm is}) = \mathbf{c}\_{0} + \mathbf{c}\_{1}\mathbf{C}\_{\rm is} + \mathbf{c}\_{2}\mathbf{C}\_{\rm is}^{2} + \mathbf{c}\_{3}\mathbf{C}\_{\rm is}^{3} + \mathbf{c}\_{4}\mathbf{C}\_{\rm is}^{4} \tag{14}$$

### **Table 4.**

*The variation of the transfer coefficient from vegetables.*


### **Table 5.**

*The variation of the transfer coefficient from fruits.*

### *3.2.1 Transfer coefficient interpolation*

The transfer coefficient was determined according to (Eq. (13)). Similar to (Eq. (14)) and the transfer coefficient (Eq. 15))was determined:

$$\mathbf{C}\_{t}(\mathbf{C}\_{it}) = \mathbf{c}\_{0} + \mathbf{c}\_{1}\mathbf{C}\_{it} + \mathbf{c}\_{2}\mathbf{C}\_{it}^{2} + \mathbf{c}\_{3}\mathbf{C}\_{it}^{3} + \mathbf{c}\_{4}\mathbf{C}\_{it}^{4} \tag{15}$$

**Table 6** shows the coefficients for the interpolation of the transfer coefficient Ct. The experimental data for the transfer coefficient indicated a potential monotonic, asymptotic decrease, the mathematical modeling was done according to formula (16):

$$\mathbf{C}\_{t}(\mathbf{C}\_{is}) = \frac{\mathbf{c}\_{0}}{\mathbf{C}\_{is}} + \mathbf{c}\_{1} \tag{16}$$

The coefficients of the polynomials (Eq. (15)), shown in **Table 7**, and those of the hyperbola (Eq. (16)), shown in **Table 6**.


### **Table 6.**

*The hyperbolic interpolation equations corresponding to the transfer coefficient.*



$$\mathbf{C}\_{\text{f}}(\mathbf{C}\_{\text{i}i}) = c\_0 + c\_1 \mathbf{C}\_{\text{i}i} + c\_2 \mathbf{C}\_{\text{i}i}^2 \tag{17}$$

*Evaluate the Impact of Soil Contamination on Vegetables and Fruits DOI: http://dx.doi.org/10.5772/intechopen.110445*


**Table 8.**

*The interpolation equations corresponding to the fruits.*
