Solve for A0 2A_0=A_0e^(kt)

$2 A_{0} = A_{0} e^{k t}$

Subtract $A_{0} e^{k t}$ from both sides of the equation.

$2 A_{0} - A_{0} e^{k t} = 0$

Factor $A_{0}$ out of $2 A_{0} - A_{0} e^{k t}$ .

Factor $A_{0}$ out of $2 A_{0}$ .

$A_{0} \cdot 2 - A_{0} e^{k t} = 0$

Factor $A_{0}$ out of $- A_{0} e^{k t}$ .

$A_{0} \cdot 2 + A_{0} (- 1 e^{k t}) = 0$

Factor $A_{0}$ out of $A_{0} \cdot 2 + A_{0} (- 1 e^{k t})$ .

$A_{0} (2 - 1 e^{k t}) = 0$

Rewrite $- 1 e^{k t}$ as $- e^{k t}$ .

$A_{0} (2 - e^{k t}) = 0$

Divide each term in $A_{0} (2 - e^{k t}) = 0$ by $2 - e^{k t}$ and simplify.

Divide each term in $A_{0} (2 - e^{k t}) = 0$ by $2 - e^{k t}$ .

$\frac{A_{0} (2 - e^{k t})}{2 - e^{k t}} = \frac{0}{2 - e^{k t}}$

Simplify the left side.

Cancel the common factor of $2 - e^{k t}$ .

Cancel the common factor.

$\frac{A_{0} (2 - e^{k t})}{2 - e^{k t}} = \frac{0}{2 - e^{k t}}$

Divide $A_{0}$ by $1$ .

$A_{0} = \frac{0}{2 - e^{k t}}$

Simplify the right side.

Divide $0$ by $2 - e^{k t}$ .

$A_{0} = 0$