Solve ae^bt=c

$$a e ^ { b t } = c$$

Solve for a

$$a=\frac{c}{e^{bt}}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$e^{bt}a=c$$

Divide both sides by e^{bt}.

$$\frac{e^{bt}a}{e^{bt}}=\frac{c}{e^{bt}}$$

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

$$a=\frac{c}{e^{bt}}$$

Solve for b

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