Solve y=ae^kx

$$y = a e ^ { k x }$$

Solve for a

$$a=\frac{y}{e^{kx}}$$

Steps for Solving Linear Equation

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

$$ae^{kx}=y$$

The equation is in standard form.

$$e^{kx}a=y$$

Divide both sides by e^{kx}.

$$\frac{e^{kx}a}{e^{kx}}=\frac{y}{e^{kx}}$$

Dividing by e^{kx} undoes the multiplication by e^{kx}.

$$a=\frac{y}{e^{kx}}$$

Solve for k

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