Solve x_{a}=x_{e}*k_{D}*1/T_{1}*e^frac{t{T_{1}}}

$$x _ { a } = x _ { e } \cdot k _ { D } \cdot \frac { 1 } { T _ { 1 } } \cdot e ^ { \frac { t } { T _ { 1 } } }$$

Solve for k_D

$$\left\{\begin{matrix}k_{D}=\frac{T_{1}x_{a}e^{-\frac{t}{T_{1}}}}{x_{e}}\text{, }&x_{e}\neq 0\text{ and }T_{1}\neq 0\\k_{D}\in \mathrm{R}\text{, }&x_{a}=0\text{ and }x_{e}=0\text{ and }T_{1}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by T_{1}.

$$x_{a}T_{1}=x_{e}k_{D}\times 1e^{\frac{t}{T_{1}}}$$

Swap sides so that all variable terms are on the left hand side.

$$x_{e}k_{D}\times 1e^{\frac{t}{T_{1}}}=x_{a}T_{1}$$

Reorder the terms.

$$k_{D}x_{e}e^{\frac{t}{T_{1}}}=T_{1}x_{a}$$

The equation is in standard form.

$$x_{e}e^{\frac{t}{T_{1}}}k_{D}=T_{1}x_{a}$$

Divide both sides by x_{e}e^{tT_{1}^{-1}}.

$$\frac{x_{e}e^{\frac{t}{T_{1}}}k_{D}}{x_{e}e^{\frac{t}{T_{1}}}}=\frac{T_{1}x_{a}}{x_{e}e^{\frac{t}{T_{1}}}}$$

Dividing by x_{e}e^{tT_{1}^{-1}} undoes the multiplication by x_{e}e^{tT_{1}^{-1}}.

$$k_{D}=\frac{T_{1}x_{a}}{x_{e}e^{\frac{t}{T_{1}}}}$$

Divide T_{1}x_{a} by x_{e}e^{tT_{1}^{-1}}.

$$k_{D}=\frac{T_{1}x_{a}e^{-\frac{t}{T_{1}}}}{x_{e}}$$