Question

$r = K.\lbrack A\rbrack^{n} \Rightarrow n = \frac{\ln(r/K)}{\ln\lbrack A\rbrack}$

Now, $\frac{r_{2}}{r_{1}} = \left( \frac{\left\lbrack A_{2} \right\rbrack}{\left\lbrack A_{1} \right\rbrack} \right)^{n} \Rightarrow n = \frac{\ln r_{2} - \ln r_{1}}{\ln\left\lbrack A_{2} \right\rbrack - \ln\left\lbrack A_{1} \right\rbrack}$

$\text{and, }t_{1/2}\alpha\left\lbrack A_{0} \right\rbrack^{1 - n} \Rightarrow \frac{\left( t_{1/2} \right)_{2}}{\left( t_{1/2} \right)_{1}} = \left( \frac{\left\lbrack A_{0} \right\rbrack_{2}}{\left\lbrack A_{0} \right\rbrack_{1}} \right)^{1 - n} $$$\therefore n = 1 - \frac{{\ln\left\lbrack A_{0} \right\rbrack}_{2} - {\ln\left\lbrack A_{0} \right\rbrack}_{1}}{{\ln\left( t_{1/2} \right)}_{2} - {\ln\left( t_{1/2} \right)}_{1}}$$