Inverse interpolation is the process of finding the values of the argument corresponding to a given value of the function when the latter is intermediate between two tabulated values. The finite differences are differences between the values of the function or the difference between the past differences. Finite differences are forward difference, backward difference and divide difference. Temperature, concentration of substrate, concentration of enzyme and other factors are affected the rate of enzymatic reaction. The concentration of substrate is the limiting factor, as the substrate concentration increases, the Enzyme reaction rate increases. Assuming a sufficient concentration of substrate is available, increasing Enzyme concentration will increase the rate of enzymatic reaction. Temperature, concentration of substrate and concentration of enzyme are increased the rate of enzymatic reaction at a limit which is called optimum limit. On the basis of this concept mathematical functions are defined. These mathematical functions are worked in "n" limit. Take the rate of enzymatic reaction is independent variable for finite differences, formulas and their estimation of errors. These formulas are used to obtaining intermediate values of Temperature, substrate concentration and enzyme concentration. If the point lies in the upper half then used forward difference interpolation. If the point lies in the lower half then used backward difference interpolation. When the interval is not equally spaced then used divide difference interpolation.

Quantitative structure-activity relationships (QSAR) attempts to find consistent relationships between the variations in the values of molecular properties and the biological activity for a series of compounds. These physicochemical descriptors, which include parameters to account for hydrophobicity, topology, electronic properties, and steric effects, are determined empirically or, more recently, by computational methods. Quantitative structure-activity relationships (QSAR) generally take the form of a linear equation where the biological activity is dependent variable. Biological activity is depended on the parameters and the coefficients. Parameters are computed for each molecule in the series. Coefficients are calculated by fitting variations in the parameters. Intermediate values of the biological activity are obtained by some formulas. These formulas are worked in tabulated values of biological activity in Quantitative structure-activity relationships. These formulas are worked in the conditions and all conditions are based on the position of the point lies in the table. Derived formulas using Newton's method for interpolation are worked in conditions which are depending on the point lies. If the point lies in the upper half then used Newton's forward interpolation formula. If the point lies in the lower half then we used Newton's backward interpolation formula. And when the interval is not equally spaced then used Newton's divide difference interpolation formula. When the tabulated values of the function are not equidistant then used Lagrangian polynomial. Mathematical expressions are derived for estimation of errors using intermediate values and formulas.

This research paper is based on the estimation of errors in the formulas which are used to obtaining intermediate values of the rate of enzymatic reaction. The rate of enzymatic reaction is affected by concentration of substrate, Temperature, concentration of enzyme and other factors. The rise in Temperature accelerates an Enzyme reaction. At certain Temperature known as the optimum Temperature the activity is maximum. The concentration of substrate is the limiting factor, as the substrate concentration increases, the Enzyme reaction rate increases. Assuming a sufficient concentration of substrate is available, increasing Enzyme concentration will increase the enzymatic reaction rate. These formulas are derived from temperature, substrate concentration and enzyme concentration based mathematical functions. These formulas are used to obtaining intermediate values of the rate of enzymatic reaction. Formulas which are derived using Newton's method for interpolation are worked in conditions which are depending on the point lies. If the point lies in the upper half then used Newton's forward interpolation formula. If the point lies in the lower half then we used Newton's backward interpolation formula. And when the interval is not equally spaced then used Newton's divide difference interpolation formula. When the tabulated values of the function are not equidistant then used Lagrangian polynomial. Mathematical expressions are derived for estimation of errors using intermediate values and formulas. All expressions are worked in n limit which is the optimum limit.