Solve f(x)=(100x+50)*e^-0,4x+0,1

$$f ( x ) = ( 100 x + 50 ) \cdot e ^ { - 0,4 x + 0,1 }$$

Solve for f

$$f=\frac{50\left(2x+1\right)e^{-\frac{2x}{5}+0,1}}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 100x+50 by e^{-0,4x+0,1}.

$$fx=100xe^{-0,4x+0,1}+50e^{-0,4x+0,1}$$

The equation is in standard form.

$$xf=100xe^{-\frac{2x}{5}+0,1}+50e^{-\frac{2x}{5}+0,1}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{50\left(2x+1\right)e^{-\frac{2x}{5}+0,1}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{50\left(2x+1\right)e^{-\frac{2x}{5}+0,1}}{x}$$

Divide 50\left(1+2x\right)e^{-\frac{2x}{5}+0,1} by x.

$$f=\frac{50\left(2x+1\right)e^{-\frac{2x}{5}+\frac{1}{10}}}{x}$$