Problem $3.$ In a small$-$scale mining project in Kalinga, mining wastewater containing lead ions

were removed using zeolite granules before the wastewater can be safely disposed of in a river

nearby. Isotherm study was carried out to determine the maximum adsorption capacity of zeolite

using the Freundlich equation. Refer to the table below for the experimental $q_e$ values and their

corresponding $C_e$ values. Use the Freundlich equation below:

$log{q}_e=log{K}_F+\frac{1}{n}loglog{C}_e$

where $y$ is $log{q}_c,x$ is $log{C}_c,log{K}_F$ is the $y-$intercept and $\frac{\text{I}}{n}$ is the slope.

Determine the following:

a$)$ Assuming that the simple linear regression model is appropriate, obtain the equation

of the estimated regression line. From the linear regression equation, what is the value

of $K_F$ and $n?(40$ points$)$

b$)$ What proportion of the observed $q_c$ can be explained by the model relationship? $(30$

points$)$

c$)$ Predict the $q_c$ value when $C_c$ is $19\mathrm{.}1.(10$ points$)$

d$)$ The authors of the article claim that there is a linear relationship between percent

absorption and peak photovoltage. Carry out a formal test. $(20$ point$)$