Solve y=a(1-e^-frac{x{h}})

$$y = a ( 1 - e ^ { - \frac { x } { h } } )$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{ye^{\frac{x}{h}}}{1-e^{\frac{x}{h}}}\text{, }&x\neq 0\text{ and }h\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }h\neq 0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a\left(1-e^{-\frac{x}{h}}\right)=y$$

Use the distributive property to multiply a by 1-e^{-\frac{x}{h}}.

$$a-ae^{-\frac{x}{h}}=y$$

Combine all terms containing a.

$$\left(1-e^{-\frac{x}{h}}\right)a=y$$

Divide both sides by 1-e^{-xh^{-1}}.

$$\frac{\left(1-e^{-\frac{x}{h}}\right)a}{1-e^{-\frac{x}{h}}}=\frac{y}{1-e^{-\frac{x}{h}}}$$

Dividing by 1-e^{-xh^{-1}} undoes the multiplication by 1-e^{-xh^{-1}}.

$$a=\frac{y}{1-e^{-\frac{x}{h}}}$$

Divide y by 1-e^{-xh^{-1}}.

$$a=\frac{ye^{\frac{x}{h}}}{e^{\frac{x}{h}}-1}$$

Solve for h

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