Solve f(t)=(25-t)*e^0,1*tm

$$f ( t ) = ( 25 - t ) \cdot e ^ { 0,1 \cdot t } m$$

Solve for f

$$\left\{\begin{matrix}f=\frac{m\left(25-t\right)e^{\frac{t}{10}}}{t}\text{, }&t\neq 0\\f\in \mathrm{R}\text{, }&m=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 25-t by e^{0,1t}.

$$ft=\left(25e^{0,1t}-te^{0,1t}\right)m$$

Use the distributive property to multiply 25e^{0,1t}-te^{0,1t} by m.

$$ft=25e^{0,1t}m-te^{0,1t}m$$

The equation is in standard form.

$$tf=25me^{\frac{t}{10}}-mte^{\frac{t}{10}}$$

Divide both sides by t.

$$\frac{tf}{t}=\frac{m\left(25-t\right)e^{\frac{t}{10}}}{t}$$

Dividing by t undoes the multiplication by t.

$$f=\frac{m\left(25-t\right)e^{\frac{t}{10}}}{t}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{fte^{-\frac{t}{10}}}{25-t}\text{, }&t\neq 25\\m\in \mathrm{R}\text{, }&f=0\text{ and }t=25\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 25-t by e^{0,1t}.

$$ft=\left(25e^{0,1t}-te^{0,1t}\right)m$$

Use the distributive property to multiply 25e^{0,1t}-te^{0,1t} by m.

$$ft=25e^{0,1t}m-te^{0,1t}m$$

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

$$25e^{0,1t}m-te^{0,1t}m=ft$$

Combine all terms containing m.

$$\left(25e^{0,1t}-te^{0,1t}\right)m=ft$$

The equation is in standard form.

$$\left(25e^{\frac{t}{10}}-te^{\frac{t}{10}}\right)m=ft$$

Divide both sides by 25e^{0,1t}-te^{0,1t}.

$$\frac{\left(25e^{\frac{t}{10}}-te^{\frac{t}{10}}\right)m}{25e^{\frac{t}{10}}-te^{\frac{t}{10}}}=\frac{ft}{25e^{\frac{t}{10}}-te^{\frac{t}{10}}}$$

Dividing by 25e^{0,1t}-te^{0,1t} undoes the multiplication by 25e^{0,1t}-te^{0,1t}.

$$m=\frac{ft}{25e^{\frac{t}{10}}-te^{\frac{t}{10}}}$$

Divide ft by 25e^{0,1t}-te^{0,1t}.

$$m=\frac{fte^{-\frac{t}{10}}}{25-t}$$