Solve y=A*e^-kt

$$y = A \cdot e ^ { - k t }$$

Solve for A

$$A=ye^{kt}$$

Steps for Solving Linear Equation

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

$$Ae^{\left(-k\right)t}=y$$

Reorder the terms.

$$Ae^{-kt}=y$$

The equation is in standard form.

$$\frac{1}{e^{kt}}A=y$$

Divide both sides by e^{-kt}.

$$\frac{\frac{1}{e^{kt}}Ae^{kt}}{1}=\frac{ye^{kt}}{1}$$

Dividing by e^{-kt} undoes the multiplication by e^{-kt}.

$$A=\frac{ye^{kt}}{1}$$

Divide y by e^{-kt}.

$$A=ye^{kt}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{\ln(\frac{y}{A})}{t}\text{, }&\left(t\neq 0\text{ and }y<0\text{ and }A<0\right)\text{ or }\left(t\neq 0\text{ and }y>0\text{ and }A>0\right)\\k\in \mathrm{R}\text{, }&\left(y=0\text{ and }A=0\right)\text{ or }\left(y=A\text{ and }t=0\text{ and }A\neq 0\right)\end{matrix}\right.$$