Solve y=Ae^-0.000427t

$$y = A e ^ { - 0.000427 t }$$

Solve for A

$$A=ye^{\frac{427t}{1000000}}$$

Steps for Solving Linear Equation

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

$$Ae^{-0.000427t}=y$$

The equation is in standard form.

$$e^{-\frac{427t}{1000000}}A=y$$

Divide both sides by e^{-0.000427t}.

$$\frac{e^{-\frac{427t}{1000000}}A}{e^{-\frac{427t}{1000000}}}=\frac{y}{e^{-\frac{427t}{1000000}}}$$

Dividing by e^{-0.000427t} undoes the multiplication by e^{-0.000427t}.

$$A=\frac{y}{e^{-\frac{427t}{1000000}}}$$

Divide y by e^{-0.000427t}.

$$A=ye^{\frac{427t}{1000000}}$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=-\frac{i\times 2000000\pi n_{1}}{427}-\frac{1000000\ln(\frac{y}{A})}{427}\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq 0\text{ and }A\neq 0\\t\in \mathrm{C}\text{, }&y=0\text{ and }A=0\end{matrix}\right.$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{1000000\ln(\frac{y}{A})}{427}\text{, }&\left(y<0\text{ and }A<0\right)\text{ or }\left(y>0\text{ and }A>0\right)\\t\in \mathrm{R}\text{, }&y=0\text{ and }A=0\end{matrix}\right.$$